Multiple Choice
What is the wavelength in nanometers of light with a frequency of 7.8 × 10^15 Hz?
9. Quantum Mechanics
Wavelength and Frequency
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What must be the velocity, in meters per second, of a beam of electrons if they are to display a de Broglie wavelength of 880 nm?
A
1.50 x 10^6 m/s
B
2.99 x 10^7 m/s
C
3.00 x 10^8 m/s
D
8.28 x 10^5 m/s
Verified step by step guidance1
Understand the de Broglie wavelength formula: \( \lambda = \frac{h}{mv} \), where \( \lambda \) is the wavelength, \( h \) is Planck's constant \( 6.626 \times 10^{-34} \text{ m}^2 \text{ kg/s} \), \( m \) is the mass of an electron \( 9.109 \times 10^{-31} \text{ kg} \), and \( v \) is the velocity.
Rearrange the formula to solve for velocity \( v \): \( v = \frac{h}{m\lambda} \).
Convert the given wavelength from nanometers to meters: \( 880 \text{ nm} = 880 \times 10^{-9} \text{ m} \).
Substitute the known values into the rearranged formula: \( v = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 880 \times 10^{-9}} \).
Calculate the velocity \( v \) using the substituted values to find the speed of the electrons in meters per second.
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