Question

Photoelectrons with a maximum speed of 8.00 × 107 m/s are ejected from a surface in the presence of light with a frequency of 7.50 × 1014Hz. If the mass of an electron is 9.10 × 10-31 kg, calculate the maximum kinetic energy of a single electron, in joules.

7.28 × 10-23 J
5.82 × 10-15 J
2.91 × 10-15 J
3.41 × 10-16 J

Answer 1

KE = 1/2 * mass * velocity^2
KE = 1/2 * 9.10x10^-31 * (8.00x10^7)^2
KE = 1/2 * 9.10x10^-13 * 6.4x10^15
KE = 2.912x10^-15 J or C

Answer 2

Maximum kinetic energy,
`E_k=2.91* 10^(-15)\ J`

Step-by-step explanation:

It is given that,

Speed of photoelectrons,
`v_(max)=8* 10^7\ m/s`

Mass of electrons,
`m=9.1* 10^(-31)\ Kg`

Frequency of light,
`\\u=7.5* 10^(14)\ Hz`

According to Einstein equation :

`h\\u=h\\u_o+(1)/(2)mv_(max)^2`

Where

υ is frequency of radiation

υ₀ is the threshold frequency

Maximum kinetic energy of single electron is,
`E_k=(1)/(2)mv_(max)^2`

`E_k=(1)/(2)* 9.1* 10^(-31)* (8* 10^7)^2`

`E_k=2.91* 10^(-15)\ J`

Hence, the correct option is (C) "
`2.91* 10^(-15)\ J` "