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Multiple Choice
A typical electron velocity is 7.27 x 10^6 m/s. Calculate the de Broglie wavelength of an electron having this velocity:
A
1.0 x 10^-10 m
B
2.5 x 10^-10 m
C
0.5 x 10^-10 m
D
1.5 x 10^-10 m
Verified step by step guidance
1
Identify the formula for the de Broglie wavelength: \( \lambda = \frac{h}{mv} \), 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 the electron \( 9.109 \times 10^{-31} \text{ kg} \), and \( v \) is the velocity of the electron.
Substitute the given velocity \( v = 7.27 \times 10^6 \text{ m/s} \) into the de Broglie wavelength formula.
Substitute the known values for Planck's constant \( h = 6.626 \times 10^{-34} \text{ m}^2 \text{ kg/s} \) and the mass of the electron \( m = 9.109 \times 10^{-31} \text{ kg} \) into the formula.
Perform the calculation by dividing Planck's constant by the product of the mass of the electron and its velocity: \( \lambda = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 7.27 \times 10^6} \).
Simplify the expression to find the de Broglie wavelength \( \lambda \) in meters.