A source of monochromatic radiation of wavelength 400 nm provides 1000 J of energy in 10 seconds. When this radiation falls on the surface of sodium, x × 10²⁰ electrons are ejected per second. Assume that wavelength 400 nm is sufficient for ejection of electron from the surface of sodium metal. The value of x is ______________. (Nearest integer)
(h = 6.626 × 10⁻³⁴ Js)

Solution

Chemistry ma’am · 3 steps

One photon ejects one electron, so electrons per second equals photons per second.

1. Energy per second. The source gives 1000 J in 10 s, so its power is 1000/10 = 100 J s⁻¹.
2. Energy of one photon. With λ = 400 nm = 4 × 10⁻⁷ m, E = hc/λ = (6.626 × 10⁻³⁴ × 3 × 10⁸)/(4 × 10⁻⁷) = 4.97 × 10⁻¹⁹ J.

   photons per second = 100/(4.97 × 10⁻¹⁹) = 2.01 × 10²⁰ s⁻¹

3. So. Each photon can eject one electron, so 2.01 × 10²⁰ electrons leave per second. The nearest integer gives x = 2.

The common slip: 20. Using the full 1000 J without dividing by 10 s gives 2.01 × 10²¹ electrons, which reads as 20, not 2.

The idea to keep. In photoelectric counting questions, divide energy per second by hc/λ. That gives photons per second, and one photon ejects at most one electron.

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