Question

15. A metal plate has a binding energy of 350.0 kJ/mol. If a photon with a wavelength of 275 nm strikes the surface, at what velocity will an electron be ejected? a. 1.75 x 106 m/s

Answer 1

Photoelectric effect is the ejection of electron from a metal surface when the photons of light hits the metal surface. The emitted electrons are known as photoelectrons. The photons of light have a characteristic energy, this energy is absorbed by the electrons. When an electron acquires the energy more than the it's binding energy, it is ejected. That means, a photon is able to eject an electron when it has energy higher or equal to the binding energy of the electron. The energy of the incident radiation is used in two ways. One part of energy is used to electron from the metal surface and the second part of the energy provides the kinetic energy to the ejected electron. The energy of the photon is given as follows: E=c Where, h is Planck's constant = 6.626x1034 J.s c is the speed of light = 3.0 x10 ms? 2 is the wavelength The binding energy of the metal is 350.0 kJ/mol = 350.0 x10 J/mol=- 350.0 x103 6.022 x 1023 Jg Wavelength of photon = 275 mm = 275 x10 m Mass of electro =9.1x10-" Kg=9.1x10-9x10'g This energy is equals to the binding energy + kinetic energy of the electron. E = binding energy+Kinetic energy be = binding energy +2mv2 1 mv - - binding energy 2x (1 – binding energy m

-binding energy m Substitute the corresponding values 6.626x10-34 J.s X3.0x108 ms -1 275 x10 m 9.1x10-31 10g v=5.56x10 m/s 350.0x103 6.022x10239 The velocity of the electron is found to be 5.56x10' m/s.