Question

1. Calculate the Work Function of a metal that has a threshold frequency of 9.54 x 1014 s-1.

answer: 63.3*10^(-20)J

2. What is the wavelength of this light in nm?

answer: 314nm

3. What would be the Kinetic Energy of an ejected photoelectron if 3.26 x 1015 s-1 light struck (hit) that same metal?

answer: 1.53*10^(-18)J

4. What would be the velocity and De Broglie Wavelength of ejected photoelectron?
answer: 1.83*10^(6)m/s

5.What is the wavelength of light (in nm) of an emitted photon if an electron dropped from the n=4 to n=2 energy level?

answer: 486nm

6. What frequency of light is required to eject an electron from the n=5 energy level?

answer: 1.32*10^(14)s

I need calculation work for these answers

Answer 1

1. Work function = h* frequency

Where h = plank's constant = 6.626 *10^-34 J/s

and frequency = 9.54 *10¹⁴ s^-1

Work function = 6.626 *10^-34 J/s * 9.54 *10¹⁴ s^-1 = 63.3 *10^-20 J

2. Wavelength = c / frequency

Where c = velocity of light = 3.0 *10⁸ m/s

So, wavelength = (3.0 *10⁸ m/s) / 9.54 *10¹⁴ s^-1 = 3.17 *10^-7 m = 317 nm

3.Energy of photon = work function + energy of ejected electron

frequency of light striked = 3.26 *10¹⁵ s^-1

Energy of light = 6.626 *10^-34 J/s * 3.26 *10¹⁵ s^-1 = 2.16 *10^-18 J

So, 2.16 *10^-18 J = 63.3 *10^-20 J + energy of ejected electron

energy of ejected electron = 1.53 *10^-18 J

4. Energy of ejected electron = 1/2mv²

m = mass of electron = 9.1 *10^-31kg

1.53 *10^-18 J = (9.1 *10^-31kg/2) v²

v² = 3.36 *10¹²

v = 1.83 *10⁶ m/s

De- Broglie wavelength = h/mv

Where m = mass of electron = 9.1 *10^-31 kg

v = velocity of electron

wavelength = (6.626 *10^-34 J/s) / ( 9.1 *10^-31 kg *1.83 *10⁶ m/s ) = 397 pm

5. wavelength of light = 1.097 *10⁷m^-1 [ 1/n_f² - 1/n_i²] .....(rydberg equation)

wavelength of light = 1.097 *10⁷m^-1 [ 1/2² - 1/4²] = 486 nm

6. Energy required = 13.6 Z² / n²

For hydrogen atoms, Z= 1

and here n = 5

So, energy required = 13.6 / 25 = 0.544 eV = 8.72 *10^-20 J ....{1eV = 1.6 *10^-19J)

Energy = h* frequency

Where h = plank's constant = 6.626 *10^-34 J/s

8.72 *10^-20 J = 6.626 *10^-34 J/s* frequency

frequency = 1.32 *10¹⁴ s^-1