If, the binding energy of electrons in a metal is (250 ~kJ / mol ), what should be the threshold frequency of the striking photons in order to free an electron from the metal surface?

Step-by-step solution

Binding energy of 1 mole of electrons (=250 ~kJ ) Binding energy of 1 electron ( aligned & =(250) / (6.022 10²³ ) kJ & =4.15 10⁻²² ~kJ & =4.15 10⁻¹⁹ ~J aligned ) Threshold energy ( (h v₀ )= ) Binding energy ( aligned h v₀ & =4.15 10⁻¹⁹ ~J or v₀ & = (4.15 10⁻¹⁹ ~J ) / h & = (4.15 10¹⁹ ~J ) (6.626 10⁻³⁴ ~J ~s ) & =6.26 10¹⁴ ~s ⁻¹ aligned ) Hence, the correct option is (a).