What is the de Broglie wavelength of an electron moving with a velocity of 1.5 x 10^6 m/s? (mass of electron = 9.11 x 10^-31 kg)
Practice Questions
1 question
Q1
What is the de Broglie wavelength of an electron moving with a velocity of 1.5 x 10^6 m/s? (mass of electron = 9.11 x 10^-31 kg)
4.86 x 10^-10 m
2.42 x 10^-10 m
1.33 x 10^-10 m
6.63 x 10^-10 m
The de Broglie wavelength λ = h/p = h/(mv). Using h = 6.63 x 10^-34 J.s, we find λ = 6.63 x 10^-34 / (9.11 x 10^-31 * 1.5 x 10^6) = 2.42 x 10^-10 m.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the de Broglie wavelength of an electron moving with a velocity of 1.5 x 10^6 m/s? (mass of electron = 9.11 x 10^-31 kg)
Solution: The de Broglie wavelength λ = h/p = h/(mv). Using h = 6.63 x 10^-34 J.s, we find λ = 6.63 x 10^-34 / (9.11 x 10^-31 * 1.5 x 10^6) = 2.42 x 10^-10 m.
Steps: 10
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: Recall 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 = 1.5 x 10^6 m/s.
Step 4: Calculate the momentum: p = (9.11 x 10^-31 kg) * (1.5 x 10^6 m/s).
Step 5: Calculate the result of the momentum: p = 1.3665 x 10^-24 kg.m/s.
Step 6: Now, substitute the value of momentum into the de Broglie wavelength formula: λ = h/p.
Step 7: Use Planck's constant h = 6.63 x 10^-34 J.s.
Step 8: Substitute the values into the formula: λ = (6.63 x 10^-34 J.s) / (1.3665 x 10^-24 kg.m/s).
Step 9: Perform the division to find λ: λ = 4.85 x 10^-10 m.
Step 10: Round the answer to the appropriate number of significant figures, if necessary.
