Question

1.) Determine the energy change (in Joules) associated with the transition from n=2 to n=4 in the Hydrogen atom.

2.) Calculate the wavelength (in nm) of the red line in the visible spectrum of excited H atoms using Bohr Theory.

3.) What is the energy (in Joules) of the X-ray radiation at 2.00x10^-10 m that are used for medical diagnosis?

4.) What is the binding energy of an electron in a photosensitive metal (in kj/mol) if the minimum frequency of light that can eject electrons from the metal is 6.3x10^14 Hz?

5.) How many photons are contained in a burst of yellow light (589nm) for a sodium lamp that contains 609 kJ of energy?

Answer 1

1.) Determine the energy change (in Joules) associated with the transition from n=2 to n=4 in the Hydrogen atom.

For Hydrogen atom,
Rydberg's constant in joule, RH = 2.18E-18 J
Energy of nth orbit of Hydrogen atom, En = -RH*(1/n^2)
Change in energy from n = 2 to n = 4, dE = E4 - E2 = -RH*(1/4^2-1/2^2) = 3/16*RH = 3/16*2.18E-18 = 0.40875E-18 J

2.) Calculate the wavelength (in nm) of the red line in the visible spectrum of excited H atoms using Bohr Theory.
Red line in the visible balmer series corresponds to transition from n=3 to n=2.
For finding wavelength we use Rydberg's constant, RH = 1.09E7 m-1
Wavelength, lambda due to transition from n=3 to n=2, 1/lambda = -RH*(1/3^2-1/2^2) = 5/36*RH = 5/36*1.09E7 = 0.1514E7 m-1
lambda = 1/0.1514E7 = 6.6E-7 m = 660 nm

3.) What is the energy (in Joules) of the X-ray radiation at 2.00x10^-10 m that are used for medical diagnosis?
Wavelength, lambda = 2.0E-10 m
Planck's constant, h = 6.626E-34    J·s
speed of light, c = 3.0E8 m/s
h*c = 1.986E-25 J·m
Energy, E = h*c/lambda = 1.986E-25/2.0E-10 = 0.993E-15 J

4) What is the binding energy of an electron in a photosensitive metal (in kJ/mol) if the minimum frequency of light that can eject electrons

from the metal is 6.3x10^14 Hz?
frequency, f = 6.3E14 Hz
Energy, E = h*f = 6.626E-34*6.3E14 = 41.74E-20 J

5) How many photons are contained in a burst of yellow light (589nm) for a sodium lamp that contains 609 kJ of energy?
wavelength, lambda = 589 nm = 589E-9 m
h*c = 1.986E-25 J·m
Energy of one photon, En = 1.986E-25/589E-9 = 3.4E-19 J
Total energy, E = 609 kJ = 6.09E5 J
No. of photons, n = E/En = 6.09E5/3.4E-19 = 1.8E23
1 mole = 6.022E23
No of photons = 1.8E23/6.022E23 = 0.3 moles