Respuesta :
Answer:
The longest wavelength is 2.19 × 10⁻⁷ m.
Explanation:
The work function (ф) is the minimum energy required to remove an electron from the surface of a metal. The minimum frequency required in a radiation to submit such energy can be calculated with the following expression.
ф = h × ν
where,
h is the Planck's constant (6.63 × 10⁻³⁴ J.s)
ν is the threshold frequency for the metal
In this case,
[tex]\nu = \frac{\phi }{h} =\frac{9.05 \times 10^{-19}J }{6.63 \times 10^{-34}J.s } =1.37 \times 10^{15}s^{-1}[/tex]
We can find the wavelength associated to this frequency using the following expression.
c = λ × ν
where,
c is the speed of light (3.00 × 10⁸ m/s)
λ is the wavelength
Then,
[tex]\lambda=\frac{c}{\nu } =\frac{3.00 \times 10^{8} m/s }{1.37 \times 10^{15} s^{-1} } =2.19 \times 10^{-7} m[/tex]
Answer: Option (A) is the correct answer.
Explanation:
The given data is as follows.
Work function ([tex]\phi[/tex]) = [tex]9.05 \times 10^{19}[/tex] J
Now, relation between work function and wavelength is as follows.
[tex]\phi = E = \frac{hc}{\lambda}[/tex]
where, h = planck's constant = [tex]6.63 \times 10^{-34}[/tex] Js
c = speed pf light = [tex]3 \times 10^{8}[/tex] m/s
[tex]\lambda[/tex] = wavelength
As work function is also known as binding energy. Therefore, putting the given values into the above formula as follows.
[tex]\phi = \frac{hc}{\lambda}[/tex]
[tex]9.05 \times 10^{19}[/tex] J = [tex]\frac{6.63 \times 10^{-34} Js \times 3 \times 10^{8}}{\lambda}[/tex]
[tex]\lambda[/tex] = [tex]\frac{19.89 \times 10^{-26}}{9.05 \times 10^{19}}[/tex]
= [tex]2.197 \times 10^{7}[/tex]
Thus, we can conclude that long wavelength of light which will cause electrons to be emitted is [tex]2.196 \times 10^{7}[/tex].
