A photon of wavelength 4 × 10–7 m strikes on metal surface, the work function of the metal being 2.13 eV. Calculate (i) the energy of the photon (eV), (ii) the kinetic energy of the emission, and (iii) the velocity of the photoelectron (1 eV= 1.6020 × 10–19 J).
(i) The energy of a photon can be calculated using the formula:
E = hc/λ
Substituting the values:
E = hc/λ
E = (6.626 x 10^-34 J s) x (299,792,458 m/s) / (4 x 10^-7 m)
E = 4.9656 x 10^-19 J
To convert Joules to electron volts (eV), we can use the conversion factor:
1 eV = 1.6020 x 10^-19 J
so, the energy of the photon in eV is:
E = (4.9656 x 10^-19 J) / (1.6020 x 10^-19 J/eV)
E = 3.1 eV
(ii) The kinetic energy of the photoelectron can be calculated using the formula:
K.E. = E - W
where E= energy of the photon and W= work function of the metal.
Substituting the values:
K.E. = (3.1 eV) - (2.13 eV)
K.E. = 0.97 eV
To convert eV to Joules, we can use the conversion factor:
1 eV = 1.6020 x 10^-19 J
Therefore, the kinetic energy of the photoelectron in Joules is:
K.E. = (0.97 eV) x (1.6020 x 10^-19 J/eV)
K.E. = 1.56 x 10^-19 J
(iii) The velocity of the photoelectron can be calculated using the formula:
K.E. = 1/2 mv^2
where m is the mass of the photoelectron and v is its velocity.
Substituting the values:
1.56 x 10^-19 J = 1/2 x (9.109 x 10^-31 kg) x v^2
Solving for v:
v = √(2K.E./m)
v = √(2 x 1.56 x 10^-19 J / 9.109 x 10^-31 kg)
v = 5.55 x 10^5 m/s
Therefore, the velocity of the photoelectron is 5.55 x 10^5 m/s.
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