+// Scilab Code Ex9.1.1:Page-411 (2008)

+clc; clear;

+u = 931.508; // Energy equivalent of 1 amu, MeV

+Z = 28; // Atomic number of ni-64

+A = 64; // Mass number of Ni-64

+m_p = 1.007825; // Mass of a proton, u

+m_n = 1.008665; // Mass of a neutron, u

+M_Ni = 63.9280; // Atomic mass of Ni-64 nucleus, u

+delta_m = Z*m_p + (A-Z)*m_n - M_Ni; // Mass difference, u

+BE = delta_m*u; // Binding energy of Ni-64 nucleus, MeV

+BE_bar = BE/A; // Binding energy per nucleon of Ni-64 nucleus, MeV

+printf("\nThe binding energy per nucleon for Ni-64 nucleus = %4.2f MeV/nucleon", BE_bar);

+

+// Result

+// The binding energy per nucleon for Ni-64 nucleus = 8.78 MeV/nucleon \ No newline at end of file

+// Scilab Code Ex9.1.2:Page-411 (2008)

+clc; clear;

+e = 1.6e-013; // Energy equivalent of 1 MeV, J

+m_p = 1.672e-027; // Mass of a proton, kg

+m_n = 1.675e-027; // Mass of a neutron, kg

+M_D = 3.343e-027; // Mass of a deutron, kg

+c = 3.00e+008; // Speed of light in vacuum, m/s

+delta_m = m_p + m_n - M_D; // Mass defect, kg

+E_B = delta_m*c^2/e; // Binding energy for the deutron, MeV

+BE_bar = E_B/2; // Binding energy per nucleon for the deutron, MeV

+printf("\nThe binding energy per nucleon for the deutron = %5.3f MeV/nucleon", BE_bar);

+

+// Result

+// The binding energy per nucleon for the deutron = 1.125 MeV/nucleon \ No newline at end of file

+// Scilab Code Ex9.1.3:Page-411 (2008)

+clc; clear;

+u = 931.508; // Energy equivalent of 1 amu, MeV

+Z = 8; // Atomic number of O-16

+A = 16; // Mass number of O-16

+m_p = 1.008142; // Mass of a proton, u

+m_n = 1.008982; // Mass of a neutron, u

+M_O = 15.994915; // Atomic mass of O-16 nucleus, u

+delta_m = Z*m_p + (A-Z)*m_n - M_O; // Mass difference, u

+BE = delta_m*u; // Binding energy of O-16 nucleus, MeV

+BE_bar = BE/A; // Binding energy per nucleon of O-16 nucleus, MeV

+delta_m = abs(M_O - A); // Mass difference, u

+PF = delta_m/A; // Packing fraction for O-16 nucleus, u

+printf("\nThe binding energy per nucleon for O-16 nucleus = %4.2f MeV/nucleon", BE_bar);

+printf("\nThe packing fraction for O-16 nucleus = %5.3e u", PF);

+

+// Result

+// The binding energy per nucleon for O-16 nucleus = 8.27 MeV/nucleon

+// The packing fraction for O-16 nucleus = 3.178e-004 u \ No newline at end of file

+// Scilab Code Ex9.1.4: Page-411 (2008)

+clc; clear;

+u = 931.508; // Energy equivalent of 1 amu, MeV

+Z = 10; // Atomic number of Ne-20

+A = 20; // Mass number of Ne-0

+m_p = 1.007825; // Mass of a proton, u

+m_n = 1.008665; // Mass of a neutron, u

+BE = 160.64; // Binding energy of Ne-20 nucleus, MeV

+M = Z*m_p + (A-Z)*m_n + Z*0.51/u - BE/u; // Atomic mass of Ne-20 nucleus, u

+printf("\nThe atomic mass of Ne = %7.4f a.m.u", M);

+

+// Result

+// The atomic mass of Ne = 19.9979 a.m.u \ No newline at end of file

+// Scilab Code Ex9.2.1: Page-414 (2008)

+clc; clear;

+h = 6.63e-034; // Planck's constant, Js

+c = 3.00e+008; // Speed of light in vacuum, m/s

+I = 1e+004; // Intensity of monochromatic beam, W/Sq.m

+nu = 1e+004; // Frequency of monochromatic beam, Hz

+n = I/(h*nu*c); // Average number of photons per cubic metre, photons/metre-cube

+printf("\nThe average number of photons in the monochromatic beam of radiation = %4.2e photons/metre-cube", n);

+

+// Result

+// The average number of photons in the monochromatic beam of radiation = 5.03e+024 photons/metre-cube \ No newline at end of file

+// Scilab Code Ex9.2.11: Page-418(2008)

+clc; clear;

+u = 931.5; // Energy equivalent of 1 amu, MeV

+m_x = 4.002603; // Mass of projectile (alpha-particle), u

+m_y = 1.007825; // Mass of emitted particle (proton), u

+M_X = 14.0031; // Mass of target nucleus (N-14), u

+M_Y = 16.9994; // Mass of daughter nucleus (O-16), u

+Q = ((m_x + M_X) - (m_y + M_Y))*u; // Q-value of the reaction, MeV

+printf("\nThe Q-value of the nuclear reaction = %5.3f MeV", Q);

+

+// Result

+// The Q-value of the nuclear reaction = -1.418 MeV \ No newline at end of file

+// Scilab Code Ex9.2.12: Page-418(2008)

+clc; clear;

+u = 931.5; // Energy equivalent of 1 amu, MeV

+// First reaction

+m_x = 1.007825; // Mass of projectile (proton), u

+m_y = 2.014102; // Mass of emitted particle (deutron), u

+M_X = 208.980394; // Mass of target nucleus (Bi-209), u

+M_Y = 207.979731; // Mass of daughter nucleus (Bi-208), u

+Q = ((m_x + M_X) - (m_y + M_Y))*u; // Q-value of the reaction, MeV

+Ex_threshold = -Q*(m_x + M_X)/M_X; // The smallest value of the projectile energy, MeV

+printf("\nThe threshhold energy of the reaction Bi(209,83) + p --> Bi(208,83) + d = %4.2f MeV", Ex_threshold);

+// Second reaction

+m_x = 4.002603; // Mass of projectile (alpha-particle), u

+m_y = 1.007825; // Mass of emitted particle (proton), u

+M_X = 27.98210; // Mass of target nucleus (Al-27), u

+M_Y = 30.973765; // Mass of daughter nucleus (P-31), u

+Q = ((m_x + M_X) - (m_y + M_Y))*u; // Q-value of the reaction, MeV

+Ex_threshold = -Q*(m_x + M_X)/M_X; // The smallest value of the projectile energy, MeV

+printf("\nThe threshhold energy of the reaction Al(27,13) + He --> P(31,15) + p = %4.2f MeV", Ex_threshold);

+

+// Result

+// The threshhold energy of the reaction Bi(209,83) + p --> Bi(208,83) + d = 5.25 MeV

+// The threshhold energy of the reaction Al(27,13) + He --> P(31,15) + p = -3.31 MeV \ No newline at end of file

+// Scilab Code Ex9.2.13: Page-418(2008)

+clc; clear;

+function p = Find(Z, A)

+ if Z == 2 & A == 4 then

+ p = 'alpha';

+ end

+ if Z == -1 & A == 0 then

+ p = 'beta-';

+ end

+ if Z == 1 & A == 0 then

+ p = 'beta+';

+ end

+endfunction

+R1 = cell(4,3);

+R2 = cell(4,3);

+// Enter data for first cell (Reaction)

+R1(1,1).entries = 'Li'; // Element

+R1(1,2).entries = 3; // Atomic number

+R1(1,3).entries = 6; // Mass number

+R1(2,1).entries = 'd';

+R1(2,2).entries = 1;

+R1(2,3).entries = 2;

+R1(3,1).entries = 'X';

+R1(3,2).entries = 0;

+R1(3,3).entries = 0;

+R1(4,1).entries = 'He';

+R1(4,2).entries = 2;

+R1(4,3).entries = 4;

+// Enter data for second cell (Reaction)

+R2(1,1).entries = "Te";

+R2(1,2).entries = 52;

+R2(1,3).entries = 122;

+R2(2,1).entries = 'X';

+R2(2,2).entries = 0;

+R2(2,3).entries = 0;

+R2(3,1).entries = 'I';

+R2(3,2).entries = 53;

+R2(3,3).entries = 124;

+R2(4,1).entries = 'd';

+R2(4,2).entries = 1;

+R2(4,3).entries = 2;

+R1(3,2).entries = R1(1,2).entries+R1(2,2).entries-R1(4,2).entries

+R1(3,3).entries = R1(1,3).entries+R1(2,3).entries-R1(4,3).entries

+particle = Find(R1(3,2).entries, R1(3,3).entries); // Find the unknown particle

+printf("\nFor the reaction\n")

+ printf("\t%s(%d) + %s(%d) --> %s + %s(%d)\n X must be an %s particle", R1(1,1).entries, R1(1,3).entries, R1(2,1).entries, R1(2,3).entries, R1(3,1).entries, R1(4,1).entries, R1(4,3).entries, particle);

+R2(2,2).entries = R2(3,2).entries+R2(4,2).entries-R2(1,2).entries

+R2(2,3).entries = R2(3,3).entries+R2(4,3).entries-R2(1,3).entries

+particle = Find(R2(2,2).entries, R2(2,3).entries); // Find the unknown particle

+printf("\n\nFor the reaction\n")

+ printf("\t%s(%d) + %s --> %s(%d)+%s(%d)\n X must be an %s particle", R2(1,1).entries, R2(1,3).entries, R2(2,1).entries, R2(3,1).entries, R2(3,3).entries, R2(4,1).entries, R2(4,3).entries, particle);

+

+// Result

+// For the reaction

+// Li(6) + d(2) --> X + He(4)

+// X must be an alpha particle

+

+// For the reaction

+// Te(122) + X --> I(124)+d(2)

+// X must be an alpha particle \ No newline at end of file

+// Scilab Code Ex9.2.14: Page-419(2008)

+clc; clear;

+h = 6.63e-034; // Planck's constant, Js

+c = 3e+008; // Speed of light, m/s

+lambda = 10e-012; // Wavelength of incident X-rays, m

+lambda_c = 2.426e-012; // Compton wavelength for the electron, m

+phi = 45; // Angle of scattering of X-rays, degree

+lambda_prime = lambda + lambda_c*(1 - cosd(phi)); // Wavelength of scattered X-rays, m

+// For maximum wavelength

+phi = 180; // Angle for maximum scattering, degree

+lambda_prime_max = lambda + lambda_c*(1 - cosd(phi)) ; // Maximum wavelength present in the scattered X-rays, m

+KE_max = h*c*(1/lambda-1/lambda_prime_max); // Maximum kinetic energy of the recoil electrons, J

+printf("\nThe wavelength of scattered X-rays = %5.2e m", lambda_prime);

+printf("\nThe maximum wavelength present in the scattered X-rays = %6.3f pm", lambda_prime_max/1e-012);

+printf("\nThe maximum kinetic energy of the recoil electrons = %5.3e J", KE_max);

+

+// Result

+// The wavelength of scattered X-rays = 1.07e-011 m

+// The maximum wavelength present in the scattered X-rays = 14.852 pm

+// The maximum kinetic energy of the recoil electrons = 6.498e-015 J \ No newline at end of file

+// Scilab Code Ex9.2.16: Page-420(2008)

+clc; clear;

+m = 3; n = 3; p = 2; // Coefficients of intercepts along three axes

+m_inv = 1/m; // Reciprocate the first coefficient

+n_inv = 1/n; // Reciprocate the second coefficient

+p_inv = 1/p; // Reciprocate the third coefficient

+mul_fact = double(lcm(int32([m,n,p]))); // Find l.c.m. of m,n and p

+m1 = m_inv*mul_fact; // Clear the first fraction

+m2 = n_inv*mul_fact; // Clear the second fraction

+m3 = p_inv*mul_fact; // Clear the third fraction

+printf("\nThe miller indices for planes with set of intercepts (%da, %db, %dc) are (%d %d %d) ", m, n, p, m1, m2, m3);

+m = 1; n = 2; p = %inf; // Coefficients of intercepts along three axes

+m_inv = 1/m; // Reciprocate the first coefficient

+n_inv = 1/n; // Reciprocate the second coefficient

+p_inv = 1/p; // Reciprocate the third coefficient

+mul_fact = double(lcm(int32([m,n]))); // Find l.c.m. of m,n and p

+m1 = m_inv*mul_fact; // Clear the first fraction

+m2 = n_inv*mul_fact; // Clear the second fraction

+m3 = p_inv*mul_fact; // Clear the third fraction

+printf("\nThe miller indices for planes with set of intercepts (%da, %db, %dc) are (%d %d %d) ", m, n, p, m1, m2, m3);

+

+// Result

+// The miller indices for planes with set of intercepts (3a, 3b, 2c) are (2 2 3)

+// The miller indices for planes with set of intercepts (1a, 2b, Infc) are (2 1 0) \ No newline at end of file

+// Scilab Code Ex9.2.19: Page-421(2008)

+clc; clear;

+d = 1; // For simplicity assume interplanar spacing to be unity, m

+theta = 15; // Glancing angle for first order, degree

+n = 1; // Order of reflection

+// From Bragg's law, 2*d*sind(theta) = n*lambda, solving for lambda

+lambda = 2*d*sind(theta)/n; // Wavelength of incident X-ray, angstrom

+// For second order reflection

+n = 2

+theta = asind(n*lambda/(2*d)); // Glancing angle for second order reflection, degree

+printf("\nThe glancing angle for the second order reflection = %4.1f degree", theta);

+// For third order reflection

+n = 3;

+theta = asind(n*lambda/(2*d)); // Glancing angle for third order reflection, degree

+printf("\nThe glancing angle for the third order reflection = %4.1f degree", theta);

+

+// Result

+// The glancing angle for the second order reflection = 31.2 degree

+// The glancing angle for the third order reflection = 50.9 degree \ No newline at end of file

+// Scilab Code Ex9.2.2: : Page-414 (2008)

+clc; clear;

+h = 6.63e-034; // Planck's constant, Js

+c = 3.00e+008; // Speed of light in vacuum, m/s

+I = 1e+004; // Intensity of monochromatic beam, W/Sq.m

+nu = 1e+004; // Frequency of monochromatic beam, Hz

+n = I/(h*nu*c); // Average number of photons per cubic metre, photons/metre-cube

+printf("\nThe average number of photons in the monochromatic beam of radiation = %4.2e photons/metre-cube", n);

+

+// Result

+// The average number of photons in the monochromatic beam of radiation = 5.03e+024 photons/metre-cube \ No newline at end of file

+// Scilab Code Ex9.2.3: Page-414 (2008)

+clc; clear;

+h = 6.63e-034; // Planck's constant, Js

+c = 3.00e+008; // Speed of light in vacuum, m/s

+e = 1.6e-019; // Energy equivalent of 1 eV, J

+m_e = 9.1e-031; // Rest mass of an electron, kg

+lambda0 = 2762e-010; // Thereshold wavelength of silver, m

+lambda = 2000e-010; // Wavelength of ultraviolet rays, m

+E_max = h*c*(1/lambda - 1/lambda0); // Maximum kinetic energy of the ejected electrons from Einstein's photoelectric equation, J

+// As E_max = 1/2*m_e*v^2, solving for v

+v_max = sqrt(2*E_max/m_e); // Maximum velocity of the photoelectrons, m/s

+V0 = E_max/e; // Stopping potential for the electrons, V

+printf("\nThe maximum kinetic energy of the ejected electrons = %5.3e J", E_max);

+printf("\nThe maximum velocity of the photoelectrons = %4.2e m/s", v_max);

+printf("\nThe stopping potential for the electrons = %5.3f V", V0);

+

+// Result

+// The maximum kinetic energy of the ejected electrons = 2.744e-019 J

+// The maximum velocity of the photoelectrons = 7.77e+005 m/s

+// The stopping potential for the electrons = 1.715 V \ No newline at end of file

+// Scilab Code Ex9.2.4: Page-415 (2008)

+clc; clear;

+lambda1 = 3333e-010; // First wavelength of the incident light, m

+lambda2 = 2400e-010; // Second wavelength of the incident light, m

+c = 3e+008; // Speed of light in free space, m/s

+e = 1.6e-019; // Energy equivalent of 1 eV, J

+E1 = 0.6; // Kinetic energy of the emitted photoelectrons for the first wavelength, eV

+E2 = 2.04; // Kinetic energy of the emitted photoelectrons for the second wavelength, eV

+h = (E2 - E1)*lambda1*lambda2*e/(c*(lambda1 - lambda2)); // Planck's constant, Js

+W0 = (E2*lambda2 - E1*lambda1)/(lambda1 - lambda2); // Work function of the metal, eV

+printf("\nThe value of Planck constant = %3.1e Js", h);

+printf("\nThe work function of the metal = %3.1f eV", W0);

+

+// Result

+// The value of Planck constant = 6.6e-034 Js

+// The work function of the metal = 3.1 eV \ No newline at end of file

+// Scilab Code Ex9.2.5: Page-415 (2008)

+clc; clear;

+c = 3e+008; // Speed of light in free space, m/s

+h = 6.63e-034; // Planck's constant, Js

+m_e = 9.11e-031; // Rest mass of an electron, kg

+lambda = 0.3; // Wavelength of incident X-ray photon, angstrom

+phi = 45; // The angle of scattering, degrees

+lambda_prime = lambda + h/(m_e*c*1e-010)*(1-cosd(phi)); // The wavelength of the scattered photon, angstrom

+printf("\nThe wavelength of the scattered photon = %6.4f angstrom", lambda_prime);

+

+// Result

+// The wavelength of the scattered photon = 0.3071 angstrom \ No newline at end of file

+// Scilab Code Ex9.2.6: Page-416 (2008)

+clc; clear;

+h = 6.63e-034; // Planck's constant, Js

+m_e = 9.11e-031; // Rest mass of an electron, kg

+e = 1.6e-019; // Energy equivalent of 1 eV, J

+K = 3*e; // Kinetic energy of the electron in metllic sodium, J

+lambda = h/sqrt(2*m_e*K)/1e-010; // de Broglie wavelength of the valence electron, angstrom

+printf("\nThe de-Broglie wavelength of the valence electron = %3.1f angstrom", lambda);

+

+// Result

+// The de-Broglie wavelength of the valence electron = 7.1 angstrom \ No newline at end of file

+// Scilab Code Ex9.2.7: Page-416 (2008)

+clc; clear;

+h = 6.63e-034; // Planck's constant, Js

+m = 9.11e-031; // Rest mass of an electron, kg

+c = 3e+008; // Speed of light in vacuum, m/s

+bita = 3/5; // Boost parameter

+v = 3/5*c; // Spped of the electron, m/s

+lambda = h/(m*v)*sqrt(1-bita^2); // de Broglie wavelength of the electron, m

+printf("\nThe de-Broglie wavelength of the moving electron = %6.4f angstrom", lambda/1e-010);

+

+// Result

+// The de-Broglie wavelength of the moving electron = 0.0323 angstrom \ No newline at end of file

+// Scilab Code Ex9.2.8: Page-416 (2008)

+clc; clear;

+h = 6.63e-034; // Planck's constant, Js

+h_bar = h/(2*%pi); // Reduced Planck's constant, Js

+delta_t = 1e-008; // Time during which the radiation is emitted, s

+delta_E = h_bar/delta_t; // Minimum uncertainty in energy of emitted light, J

+// As delta_E = h*delta_nu from Planck's quantum theory, solving for delta_nu

+delta_nu = delta_E/h; // Minimum uncertainty in frequency of emitted light, Hz

+printf("\nThe minimum uncertainty in energy of emitted light = %5.3e J", delta_E);

+printf("\nThe minimum uncertainty in frequency of emitted light = %4.2e Hz", delta_nu);

+

+// Result

+// The minimum uncertainty in energy of emitted ligh = 1.055e-026 J

+// The minimum uncertainty in frequency of emitted ligh = 1.59e+007 Hz \ No newline at end of file

+// Scilab Code Ex9.2.9: Page-417 (2008)

+clc; clear;

+h = 6.63e-034; // Planck's constant, Js

+c = 3e+008; // Speed of light in free space, m/s

+e = 1.6e-019; // Energy equivalent of 1 eV, J

+V = 50000; // Accelerating potential, V

+lambda_min = h*c/(e*V); // The shortest wavelength present in the radiation from an X-ray machine, m

+printf("\nThe shortest wavelength present in the radiation from an X-ray machine = %6.4f nm", lambda_min/1e-009);

+

+// Result

+// The shortest wavelength present in the radiation from an X-ray machine = 0.0249 nm \ No newline at end of file