What is the de Broglie wavelength of an electron moving with a velocity of 1 x 1

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Question: What is the de Broglie wavelength of an electron moving with a velocity of 1 x 10^6 m/s? (mass of electron = 9.11 x 10^-31 kg) (2022)

Options:

Correct Answer: 6.63 x 10^-24 m

Exam Year: 2022

Solution:

λ = h / p = h / (mv) = 6.63 x 10^-34 / (9.11 x 10^-31 * 1 x 10^6) = 6.63 x 10^-24 m.

What is the de Broglie wavelength of an electron moving with a velocity of 1 x 10^6 m/s? (mass of electron = 9.11 x 10^-31 kg) (2022)

What is the de Broglie wavelength of an electron moving with a velocity of 1 x 10^6 m/s? (mass of electron = 9.11 x 10^-31 kg) (2022)

Step 1: Identify the formula for de Broglie wavelength, which is λ = h / p, where h is Planck's constant and p is momentum.
Step 2: Understand that momentum (p) can be calculated using the formula p = mv, where m is mass and v is velocity.
Step 3: Substitute the values into the momentum formula. Here, m = 9.11 x 10^-31 kg and v = 1 x 10^6 m/s.
Step 4: Calculate the momentum: p = (9.11 x 10^-31 kg) * (1 x 10^6 m/s).
Step 5: Calculate the result of the momentum: p = 9.11 x 10^-25 kg m/s.
Step 6: Now, substitute the values into the de Broglie wavelength formula: λ = h / p.
Step 7: Use Planck's constant, h = 6.63 x 10^-34 J s, and substitute it into the formula: λ = 6.63 x 10^-34 / (9.11 x 10^-25).
Step 8: Perform the division to find λ: λ = 6.63 x 10^-34 / 9.11 x 10^-25 = 6.63 x 10^-24 m.

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