Answer : The maximum number of electrons released = [tex]1.432\times 10^{12}electrons[/tex]
Explanation : Given,
Frequency = [tex]4.07\times 10^{15}s^{-1}[/tex]
Kinetic energy = [tex]3.30\times 10^{-19}J[/tex]
Total energy = [tex]3.39\times 10^{-7}J[/tex]
First we have to calculate the work function of the metal.
Formula used :
[tex]K.E=h\nu -w[/tex]
where,
K.E = kinetic energy
h = Planck's constant = [tex]6.626\times 10^{-34}J/s[/tex]
[tex]\nu[/tex] = frequency
w = work function
Now put all the given values in this formula, we get the work function of the metal.
[tex]3.30\times 10^{-19}J=(6.626\times 10^{-34}J/s\times 4.07\times 10^{15}s^{-1})-w[/tex]
By rearranging the terms, we get
[tex]w=2.367\times 10^{-18}J[/tex]
Therefore, the works function of the metal is, [tex]2.367\times 10^{-18}J[/tex]
Now we have to calculate the maximum number of electrons released.
The maximum number of electrons released = [tex]\frac{\text{ Total energy}}{\text{ work function}}[/tex]
The maximum number of electrons released = [tex]\frac{3.39\times 10^{-7}J}{2.367\times 10^{-19}J}=1.432\times 10^{12}electrons[/tex]
Therefore, the maximum number of electrons released is [tex]1.432\times 10^{12}electrons[/tex]
