Question

A laser of wavelength 200 nm is incident on a metal surface, which causes the ejection of electrons. The stopping potential is measured to be 1.66 V.

Use the table below to identify the metal.

Copper

Sodium

Aluminum

Iron

Tungsten

Answer 1

Work function of a metal (ϕ) is defined as the amount of energy required to eject an electron from surface of metal.

The energy incident on metal is used to eject electron from metal (equal to work function of metal ϕ) and remaining energy is utilised in kinetic energy of electron

i,e let E be incident energy ,ϕ be work function and V be kinetic energy or eV be stopping potential

E=ϕ +eV

energy incident is E=h? [using planks equation]

==> E=hc/? [since ?=c/? and h=6.62607015 × 10⁻³⁴ joule second. and c=3*10⁸ and ?=200nm ]

submitting values E= (6.62607015 × 10⁻³⁴ *3*10⁸ )/200*10^-9 =9.9*10^-19 J/photon=6.179 eV

[since,1J=6.241509⋅10¹⁸ eV]

submitting stopping potential V=1.66V

ϕ=E-eV => 6.179-1.66=4.519eV [it is requested not to confuse with V (stopping potential)with V (volts)]

Assumption :

As question is it guess the metal and work functions are not provided we consider values from reference

metal workfunction (eV)

Copper 4.53 – 5.10

Sodium 2.36

Aluminum   4.06 – 4.26

Iron 4.67 – 4.81

Tungsten .32 – 5.22

So our calculated values match with copper ,so the metal is copper