The wavelength of electrons accelerated from rest through a potential difference of 40 kV is x × 10⁻¹² m. The value of x is ___________. (Nearest integer)
Give : Mass of electron = 9.1 × 10⁻³¹ kg
Charge on an electron = 1.6 × 10⁻¹⁹ C
Planck's constant = 6.63 × 10⁻³⁴ Js

Solution

Chemistry ma’am · 4 steps

The field hands the electron energy eV. Turn that into momentum, and de Broglie gives the wavelength.

1. Energy to momentum. An electron starting from rest and falling through V volts gains kinetic energy eV. Since K = p²/2m, its momentum is p = √2meV.

   λ = h/p = h/√2meV

2. Find the momentum. 2meV = 2 × 9.1 × 10⁻³¹ × 1.6 × 10⁻¹⁹ × 4 × 10⁴ = 1.165 × 10⁻⁴⁴. Its square root is p = 1.079 × 10⁻²² kg m s⁻¹.
3. Find the wavelength. λ = (6.63 × 10⁻³⁴)/(1.079 × 10⁻²²) = 6.14 × 10⁻¹² m.
4. So. λ ≈ 6.14 × 10⁻¹² m, so x rounds to 6.

The common slip: 9. Dropping the 2 and using p = √meV gives λ = 8.69 × 10⁻¹² m, which rounds to 9, not 6.

The idea to keep. For a charged particle accelerated from rest, use λ = h/√2mqV. Write kV as volts before you put the numbers in.

Answer from the NTA final answer key. Solution by PrepWiser.