Answer :
The work function of this metal is, [tex]21.7504\times 10^{-19}J[/tex]
The maximum number of electrons released = [tex]2.924\times 10^{11}electrons[/tex]
Solution : Given,
Frequency = [tex]4.08\times 10^{15}s^{-1}[/tex]
Kinetic energy = [tex]5.30\times 10^{-19}J[/tex]
Total energy = [tex]6.63\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]6.63\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]5.30\times 10^{-19}J=(6.63\times 10^{-34}J/s\times 4.08\times 10^{15}s^{-1})-w[/tex]
By rearranging the terms, we get
[tex]w=21.7504\times 10^{-19}J[/tex]
Therefore, the works function of the metal is, [tex]21.7504\times 10^{-19}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{6.63\times 10^{-7}J}{21.7504\times 10^{-19}J}=0.2924\times 10^{12}=2.924\times 10^{11}electrons[/tex]
Therefore, the maximum number of electrons released = [tex]2.924\times 10^{11}electrons[/tex]
The work function of metal was 21.7504 [tex]\rm \times\;10^-^1^9[/tex] J, and the maximum number of electrons ejected are 2.924 [tex]\rm \times\;10^1^1[/tex] electrons.
Kinetic energy = Plank's constant [tex]\times[/tex] frequency of wavelength - work function
From the given,
5.30 [tex]\rm \times\;10^-^1^9[/tex] J = 6.63 [tex]\rm \times\;10^-^3^4[/tex] J/s [tex]\times[/tex] 4.08 [tex]\rm \times\;10^-^1^5[/tex] [tex]\rm s^-^1[/tex] - work function
Work function = 21.7504 [tex]\rm \times\;10^-^1^9[/tex] J
The maximum number of electrons ejected: [tex]\rm \frac{total\;energy}{work\;function}[/tex]
Maximum number of electrons ejected = [tex]\rm \frac{6.36\;\times\;\;10^-^7\;J}{21.7504\;\times\;10^-^1^9\;J}[/tex]
Maximum number of electrons ejected = 2.924 [tex]\rm \times\;10^1^1[/tex] electrons.
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