Question

The binding energy for electrons in cesium is 3.43 x 10^-19 J. What colors of light will eject electrons from cesium . Answer: yellow and shorter wavelenghts. How do I know. Also, If the uncertainty in the position of sodium atom were 10^-4 meter what is the uncertainty in its speed. Please explain. I'm unsure of what is meant by uncertainty.

Answer 1

Binding energy = 3.43 * 10^-19 J

Binding energy = hv₀

Where, h = planck's constant and v₀ = threshold frequency

v₀ = (3.43 * 10^-19) / 6.625 * 10^-34

v₀ = 5.177 * 10¹⁴

wavelength = c / v₀

where, c = speed of light

wavelength = (3 * 10⁸) / (5.177 * 10¹⁴)

= 5.79 * 10^-7

And this wavelength corresponds to Yellow color.

Using Heisenberg's Uncertainty principle

ΔpΔx = h

Where, Δp is uncertainty in momentum and Δ is uncertainty in postion and h is planck's constant.

m*Δv*Δx = h

Δv = 6.625 * 10^-34 / (10^-4 * 23 * 10^-8)

= 2.88 * 10^-23