Part A Find the wavelength of the photon emitted when hydrogen makes a transitio
ID: 1303134 • Letter: P
Question
Part A
Find the wavelength of the photon emitted when hydrogen makes a transition n = 8 ? 5.
Express your answer to four significant figures and include the appropriate units.
Part B
Find the wavelength of the photon emitted when hydrogen makes a transition n = 7 ? 1.
Express your answer to four significant figures and include the appropriate units.
Part C
Find the wavelength of the photon emitted when hydrogen makes a transition n = 11 ? 2.
Express your answer to four significant figures and include the appropriate units.
Explanation / Answer
Recall, the Rydberg formula for the energy of the emitted photon that undergoes a transition between two energy levels.
E(photon) = Eo[1 / (n1)^2 - 1/(n2)^2]
where n1<n2
We also have the Plank/Einstein relation
E = h f
where E = photon energy (J); h = Plank's constant (Js); f = frequency of photon (Hz)
So lets have a go at getting the energy of the emitted photon.
Using the Rydberg formula
E(emitted photon) = - 13.6 ( 1/9 - 1/100) = 1.375 eV
To get the frequency we need to convert the eV into joules. So
1.375 * 1.6 * 10^-19 = 2.2 * 10^-19 J
From the Einstein/Plank relation we get
f = E/h
f = 2.2 * 10^-19 / 6.63 * 10^-34 = 0.331 * 10^15 = 3.31 * 10^14 Hz
From wave mechanics we have
v = f ?
? = v/f = 3.0 * 10^8 / 3.31 * 10^14 = 9.04 * 10^-6 m
? = 9.04 * 10^3 nm
So, to summarise,
a) Wavelength = 9.04 * 10^3 nm
b) Frequency = 3.31 * 10^14 Hz
c) Energy of emitted electron = 1.375 eV