The threshold frequency v₀ for a metal is 7.0 X 10¹⁴s^-1. Calculate the kinetic energy of an electron emitted when radiation of frequency v = 1.0 X 10¹⁵ s^-1 hits the metal.

Solution

According to Einstein equation.

Kinetic space Energy space space equals space 1 half straight m subscript straight e straight v squared space equals space straight h left parenthesis straight v minus straight v subscript 0 right parenthesis

Substituting the values, we have

straight K. straight E. space equals space left parenthesis 6.626 space cross times 10 to the power of negative 34 end exponent J s right parenthesis space left parenthesis 1.0 space cross times space 10 to the power of 15 straight s to the power of negative 1 end exponent space minus 7.0 space cross times space 10 to the power of 14 straight s to the power of negative 1 end exponent right parenthesis

equals space left parenthesis 6.626 space cross times space 10 to the power of 34 Js right parenthesis space cross times left parenthesis 10.0 space cross times space 10 to the power of 14 straight s to the power of negative 1 end exponent space minus 7.0 space cross times space 10 to the power of 14 straight s to the power of negative 1 end exponent right parenthesis equals space left parenthesis 6.626 space cross times 10 to the power of negative 34 end exponent Js right parenthesis space cross times space left parenthesis 3.0 space cross times space 10 to the power of 14 straight s to the power of negative 1 end exponent right parenthesis space equals space 1.988 space cross times space 10 to the power of negative 19 end exponent straight J

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