I have this question from an old exam for review. I tried the question but can't get the right answers.

An electron in an electronically excited hydrogen atom undergoes a transition from a 6d to a 2p orbital, resulting in the emission of a photon. The photon strikes a metal surface where it is absorbed,causing an electron to be ejected having a kinetic energy of 1.32×10-19J.

(a) What is the energy (in J) of the photon emitted by the hydrogen atom?

(b)What is the wavelength (in nm) of the photon emitted by the hydrogen atom?

(c) What is the minimum energy needed to remove an electron from the metal surface?

(d) The wavelength (in nm) of the ejected electron?

To start, an electron transition from a 6d to a 2p is forbidden because it violates the selection rule of delta l = +/- 1; however, if you will provide the answers that you say you can't get, I'll give it a shot.

I made a huge mistake. I guess I can't count. d electrons have l = 3 while p electrons have l = 2 so delta l is 1 and there is no violation. When I first read the problem I got it in my mind that the difference was 2. Funny thing about hour minds.

I figured out question A and B, now I am stuck at question C and D. The answers for question C is 3.52x10^-19 J and D is 1.35nm

You need the answer to a to solve d. So I obtained 4.846E-19 J for the energy of the transition (part a).

b. That translates to 410.2 nm for the wavelength.
c. K.E. = hc/wavelength - work function.
You know K.E. is 1.32E-19J. You know hc/wavelength from part a. Solve for work function which is the minimum energy required to eject an electrons.

d. You know K.E. K.E. = 1/2 mv^2. You know m (mass electron), solve for v. Then use the De Broglie equation.
wavelength = h/mv.

How did you calculate the energy for a. what formulas did you use

To solve this problem, we need to use the principles of energy conservation and the relationships given by quantum mechanics. Here is how you can approach each part of the question:

(a) What is the energy (in J) of the photon emitted by the hydrogen atom?

To calculate the energy of the emitted photon, we need to find the energy difference between the initial and final electron energy levels. The formula for the energy of a photon is given by:

E = hf

Where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J·s), and f is the frequency of the photon. Since we want the energy in Joules, we need to find the frequency.

The energy difference between the two energy levels can be obtained using the Rydberg formula:

ΔE = Rh * (1/n²f - 1/n²i)

Where Rh is the Rydberg constant (2.179 x 10^-18 J), n_i is the initial energy level, and n_f is the final energy level.

In this case, the initial energy level is 6d (with n_i = 6) and the final energy level is 2p (with n_f = 2). Substitute these values into the Rydberg formula to find ΔE. Then, using the value of ΔE, substitute it into the energy formula (E = hf) to find the energy of the photon.

(b) What is the wavelength (in nm) of the photon emitted by the hydrogen atom?

To find the wavelength, we can use the equation:

λ = c/f

Where λ is the wavelength, c is the speed of light (3.00 x 10^8 m/s), and f is the frequency of the photon. Remember that frequency is directly related to the energy of the photon (E = hf). You can use the energy from part (a) to calculate the frequency and then substitute it into the wavelength equation.

(c) What is the minimum energy needed to remove an electron from the metal surface?

The minimum energy required to remove an electron from the metal surface is known as the work function (symbolized as φ). This energy is usually given in electron volts (eV) or Joules (J). The work function can be determined by subtracting the kinetic energy of the ejected electron (given as 1.32 x 10^-19 J) from the energy of the absorbed photon (found in part a).

φ = E(absorbed photon) - KE(ejected electron)

(d) What is the wavelength (in nm) of the ejected electron?

To find the wavelength of the ejected electron, we can use de Broglie's wavelength equation. This equation states that the wavelength of a particle is given by:

λ = h / p

Where λ is the wavelength, h is Planck's constant (6.626 x 10^-34 J·s), and p is the momentum of the particle. The momentum of the ejected electron can be calculated using the following equation:

p = sqrt(2mKE)

Where p is the momentum, m is the mass of the electron (9.109 x 10^-31 kg), and KE is the kinetic energy of the ejected electron. Use this equation to find the momentum and then substitute it into the de Broglie wavelength equation to calculate the wavelength.