I have a question from an old exam that I need help to understand, i'm not sure where to start
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 understand this problem, we first need to review some basic concepts related to atomic energy levels and the behavior of photons.
1. Energy levels: In an atom, electrons can occupy different energy levels or orbitals. These energy levels are quantized, meaning they have specific discrete values.
2. Electron transitions: When an electron in an atom undergoes a transition from one energy level to another, it absorbs or emits a photon. If an electron moves to a lower energy level, it emits a photon, and if it moves to a higher energy level, it absorbs a photon.
Now, let's break down each part of the question to understand how to find the answers.
(a) What is the energy (in J) of the photon emitted by the hydrogen atom?
To find the energy of the emitted photon, we need to calculate the energy difference between the initial and final energy levels of the electron transition. The energy of a photon can be calculated using the formula:
E = h * f
where E is the energy, h is Planck’s constant (6.626 x 10^-34 J s), and f is the frequency of the photon.
The energy difference between the two energy levels can be determined from the electron configuration notation. In this case, the transition is from 6d to 2p. We know that the energy level decreases as the principal quantum number (n) increases. Hence, the transition from 6d to 2p means that the electron is moving to a lower energy level.
(b) What is the wavelength (in nm) of the photon emitted by the hydrogen atom?
The wavelength of a photon can be calculated using the formula:
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.
We can use the frequency value calculated in part (a) to find the wavelength.
(c) What is the minimum energy needed to remove an electron from the metal surface?
This question is related to the concept of the work function of a metal. The work function (W) represents the minimum amount of energy required to remove an electron from the metal surface.
The work function can be calculated using the equation:
W = E_photon - KE_ejected
where W is the work function, E_photon is the energy of the absorbed photon, and KE_ejected is the kinetic energy of the ejected electron.
(d) The wavelength (in nm) of the ejected electron?
To find the wavelength of the ejected electron, we need to use the de Broglie wavelength equation:
λ = h / p
where λ is the wavelength, h is Planck’s constant, and p is the momentum of the electron.
To calculate the momentum, we need to know the mass and velocity of the ejected electron. However, this information is not given in the question. Therefore, we cannot answer part (d) without additional information.
Now you have a step-by-step guide on how to approach this problem. You can use these explanations to solve each part of the question. If you have any specific numbers or values given in the question, please provide them so that I can help you further.