Multiple Choice
What is the frequency of a helium-neon laser light with a wavelength of 632.8 nm? The speed of light is 3.00 x 10^8 m/s.
9. Quantum Mechanics
Wavelength and Frequency
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What is the wavelength, in nanometers, of a photon with 5.11 × 10⁻¹⁹ J of energy?
A
650 nm
B
387 nm
C
500 nm
D
750 nm
Verified step by step guidance1
Start by recalling the formula that relates the energy of a photon to its wavelength: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy of the photon, \( h \) is Planck's constant \( (6.626 \times 10^{-34} \text{ J s}) \), \( c \) is the speed of light \( (3.00 \times 10^8 \text{ m/s}) \), and \( \lambda \) is the wavelength.
Rearrange the formula to solve for wavelength \( \lambda \): \( \lambda = \frac{hc}{E} \).
Substitute the given values into the equation: \( h = 6.626 \times 10^{-34} \text{ J s} \), \( c = 3.00 \times 10^8 \text{ m/s} \), and \( E = 5.11 \times 10^{-19} \text{ J} \).
Calculate \( \lambda \) using the substituted values. Ensure that the units are consistent, and the result will be in meters.
Convert the wavelength from meters to nanometers by multiplying the result by \( 1 \times 10^9 \) (since 1 meter = 1,000,000,000 nanometers).
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