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 answer these questions, we need to understand the concepts related to electronic transitions, photon energy, kinetic energy, and minimum energy required to remove an electron from a metal surface.
(a) To find the energy of the photon emitted by the hydrogen atom, we can use the formula:
E = E_initial - E_final
In this case, the transition is from a 6d to a 2p orbital. The energy of an electron in a hydrogen atom is given by the formula:
E = - 13.6 eV / n^2
where n is the principal quantum number.
For the initial state, n_initial = 6, and for the final state, n_final = 2.
Plugging these values into the formula, we can calculate the initial and final energies, and then find the energy of the photon emitted.
(b) To find the wavelength of the photon emitted, we can use the equation:
E = hc / λ
where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (2.998 x 10^8 m/s), and λ is the wavelength of the photon.
By rearranging the equation, we can solve for λ.
(c) To find the minimum energy needed to remove an electron from the metal surface, we need to consider the work function of the metal. The work function is the minimum energy required to remove an electron from the surface of a metal.
(d) To find the wavelength of the ejected electron, we can use the de Broglie wavelength equation:
λ = h / (mv)
where λ is the wavelength, h is Planck's constant, m is the mass of the electron, and v is the velocity of the electron.
By plugging in the values for Planck's constant and the mass and velocity of the electron, we can calculate the wavelength.