Multiple Choice
An electron in the n=7 level of the hydrogen atom relaxes to a lower energy level, emitting light with a wavelength of 93.1 nm. What is the value of n for the level to which the electron relaxed?
9. Quantum Mechanics
Bohr Model
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Recall that m=2 in the Balmer series. What is the energy in kJ/mol of ultraviolet light in the Balmer series corresponding to a value of n=7?
A
98.0 kJ/mol
B
109.0 kJ/mol
C
120.0 kJ/mol
D
82.0 kJ/mol
Verified step by step guidance1
Understand that the Balmer series describes the emission of light when an electron in a hydrogen atom transitions from a higher energy level (n) to n=2. In this problem, the electron transitions from n=7 to n=2.
Use the Rydberg formula to calculate the wavelength of the emitted light: \( \frac{1}{\lambda} = R_H \left( \frac{1}{m^2} - \frac{1}{n^2} \right) \), where \( R_H \) is the Rydberg constant for hydrogen (approximately \( 1.097 \times 10^7 \) m\(^{-1}\)), \( m = 2 \), and \( n = 7 \).
Calculate the wavelength \( \lambda \) using the values for \( m \) and \( n \) in the Rydberg formula. This will give you the wavelength of the emitted light in meters.
Convert the wavelength to energy using the formula \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \) J·s) and \( c \) is the speed of light (\( 3.00 \times 10^8 \) m/s). This will give you the energy in joules per photon.
Convert the energy from joules per photon to kilojoules per mole by multiplying by Avogadro's number (\( 6.022 \times 10^{23} \) mol\(^{-1}\)) and converting to kilojoules. This will give you the energy in kJ/mol.
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