Question

5. A beam of photons with a minimum energy of 222 kJ/mol can eject electrons from a potassium surface. Estimate the range of wavelengths of light that can be used to cause this phenomenon. Show your calculations with units of measure (dimensional analysis) and briefly explain your reasoning.

Answer 1

Answer: The range of wavelengths of light that can be used to cause given phenomenon is $8.953 \times 10^{21} m$.

Explanation:

Given: 222 kJ/mol (1 kJ = 1000 J) = 222000 J

Formula used is as follows.

$E = \frac{hc}{\lambda}$

where,

E = energy

h = Planck's constant = $6.625 \times 10^{-25} Js$

c = speed of light = $3 \times 10^{8} m/s$

Substitute the values into above formula as follows.

$E = \frac{hc}{\lambda}\\222000 J = \frac{6.625 \times 10^{-34}Js \times 3 \times 10^{8} m/s}{\lambda}\\\lambda = 8.953 \times 10^{21} m$

Thus, we can conclude that the range of wavelengths of light that can be used to cause given phenomenon is $8.953 \times 10^{21} m$.