Let's answer each part of the question step-by-step.
i. Calculate the maximum wavelength of electromagnetic radiation which will cause an electron to be emitted from the Zinc surface.
To find the maximum wavelength of the electromagnetic radiation that will cause an electron to be emitted from the Zinc surface, we can use the formula which relates the energy, wavelength, Planck's constant, and the speed of light:
[tex]\[ E = \frac{hc}{\lambda} \][/tex]
Where:
- [tex]\( E \)[/tex] is the energy required to emit an electron [tex]\( (6.9 \times 10^{-19} \text{ J}) \)[/tex].
- [tex]\( h \)[/tex] is Planck's constant [tex]\( (6.626 \times 10^{-34} \text{ Js}) \)[/tex].
- [tex]\( c \)[/tex] is the speed of light [tex]\( (3 \times 10^8 \text{ m/s}) \)[/tex].
- [tex]\( \lambda \)[/tex] is the wavelength.
Rearranging the formula to solve for the wavelength ([tex]\( \lambda \)[/tex]):
[tex]\[ \lambda = \frac{hc}{E} \][/tex]
Plugging in the values:
[tex]\[ \lambda = \frac{(6.626 \times 10^{-34} \text{ Js}) \times (3 \times 10^8 \text{ m/s})}{6.9 \times 10^{-19} \text{ J}} \][/tex]
Calculating this gives:
[tex]\[ \lambda = 2.8808695652173916 \times 10^{-7} \text{ m} \][/tex]
So, the maximum wavelength of electromagnetic radiation that will cause an electron to be emitted from the Zinc surface is [tex]\( 2.88 \times 10^{-7} \text{ m} \)[/tex].
ii. What would be the effect of irradiating the Zinc surface with radiation of wavelength [tex]\(4 \times 10^{-7} \text{ m}\)[/tex]? Justify your answer.
First, let's determine the energy of the electromagnetic radiation with a wavelength of [tex]\(4 \times 10^{-7} \text{ m}\)[/tex]. We use the same formula:
[tex]\[ E = \frac{hc}{\lambda} \][/tex]
Plugging in the values:
[tex]\[ E = \frac{(6.626 \times 10^{-34} \text{ Js}) \times (3 \times 10^8 \text{ m/s})}{4 \times 10^{-7} \text{ m}} \][/tex]
Calculating this gives:
[tex]\[ E = 4.9695 \times 10^{-19} \text{ J} \][/tex]
We compare this energy with the minimum energy required to emit an electron from the Zinc surface ([tex]\(6.9 \times 10^{-19} \text{ J}\)[/tex]).
Since [tex]\(4.9695 \times 10^{-19} \text{ J}\)[/tex] (the energy of the incident radiation) is less than [tex]\(6.9 \times 10^{-19} \text{ J}\)[/tex] (the minimum energy required), the incident energy is insufficient to cause an electron to be emitted.
Therefore, the effect of irradiating the Zinc surface with radiation of wavelength [tex]\(4 \times 10^{-7} \text{ m}\)[/tex] will be no emission of electron will occur. This is because the energy of the incident radiation is less than the minimum energy required to release an electron from the surface.
