What is the wavelength of an electron moving with a velocity of 1 x 10^6 m/s? (h = 6.626 x 10^-34 J·s)
Practice Questions
1 question
Q1
What is the wavelength of an electron moving with a velocity of 1 x 10^6 m/s? (h = 6.626 x 10^-34 J·s)
6.63 x 10^-28 m
6.63 x 10^-34 m
6.63 x 10^-22 m
6.63 x 10^-30 m
Using de Broglie's equation, λ = h/p; p = mv = (9.11 x 10^-31 kg)(1 x 10^6 m/s). λ = 6.626 x 10^-34 / (9.11 x 10^-31)(1 x 10^6) = 6.63 x 10^-28 m.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the wavelength of an electron moving with a velocity of 1 x 10^6 m/s? (h = 6.626 x 10^-34 J·s)
Solution: Using de Broglie's equation, λ = h/p; p = mv = (9.11 x 10^-31 kg)(1 x 10^6 m/s). λ = 6.626 x 10^-34 / (9.11 x 10^-31)(1 x 10^6) = 6.63 x 10^-28 m.
Steps: 7
Step 1: Identify the given values. We have the Planck's constant (h = 6.626 x 10^-34 J·s) and the velocity of the electron (v = 1 x 10^6 m/s).
Step 2: Find the mass of the electron. The mass (m) of an electron is approximately 9.11 x 10^-31 kg.
Step 3: Calculate the momentum (p) of the electron using the formula p = mv. Multiply the mass of the electron by its velocity: p = (9.11 x 10^-31 kg) * (1 x 10^6 m/s).
Step 4: Substitute the values into the momentum formula: p = 9.11 x 10^-25 kg·m/s.
Step 5: Use de Broglie's equation to find the wavelength (λ). The equation is λ = h/p.
Step 6: Substitute the values into de Broglie's equation: λ = (6.626 x 10^-34 J·s) / (9.11 x 10^-25 kg·m/s).
Step 7: Perform the division to find the wavelength: λ = 6.63 x 10^-28 m.
