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In the photoelectric effect, electrons are ejected from a metal surface when light strikes it. A certain minimum energy, Emin, is required to eject an electron. Any energy absorbed beyond that minimum gives kinetic energy to the electron. It is found that when light at a wavelength of 540 nm falls on a cesium surface, an electron is ejected with a kinetic energy of 260 x 10-20 1 When the wavelength is 400 nm, the kinetic energy is 1.54 x 10-19 J. (a) Calculate Emin for cesium in joules. (b) Calculate the longest wavelength, in nanometers, that will eject electrons from cesium.

Respuesta :

Answer:

A) E_min = 36.21 × 10^(-20) J

B) 549 nm

Explanation:

A) The formula for energy of a photon is given as;

E = hc / λ

Where;

h is Planck's constant = 6.626 x 10^(-34) J.s

c is the speed of light = 3 × 10^(8) m/s

λ is wavelength

Wavelength is given as; 540 nm = 540 × 10^(-9) m

Thus;

E = (6.626 × 10^(-34) × 3 × 10^(8))/(540 × 10^(-9))

E = 36.81 × 10^(-20) J

We are given kinetic energy as;2.60 x 10^(-20) J

Now formula for E_min is;

E_min = E - K.E

E_min = (36.81 × 10^(-20)) - (2.60 x 10^(-20))

E_min = 36.21 × 10^(-20) J

B) the longest wavelength, in nanometers, that will eject electrons from cesium would have an energy that would be equal to E_min.

Thus,

36.21 × 10^(-20) = (6.626 × 10^(-34) × 3 × 10^(8))/λ

Making λ the subject gives;

λ = (6.626 × 10^(-34) × 3 × 10^(8))/36.21 × 10^(-20) = 549 x 10(-9) = 549 nm

The minimum energy of the electron is [tex]E_{min} = 34.2 \times 10^{(-20)} \;\rm J.[/tex]

The longest wavelength of the electron is 549 nm.

Given that, in the photoelectric effect, electrons are ejected from a metal surface when light strikes it. A certain minimum energy, Emin, is required to eject an electron. Also given wavelength of the light is 540 nm. The kinetic energy ejected by the electron is 260 x 10-20 J.

When the wavelength is 400 nm, the kinetic energy is 1.54 x 10-19 J.

The energy of the electron can be calculated as,

[tex]E = hc/\lambda[/tex]

Where, [tex]E[/tex] is the energy of the electron, [tex]h=6.626\times10^{(-34)} \;\rm Js[/tex] is plank's constant, [tex]c[/tex] is the speed of light that is [tex]3 \times 10^8 \;\rm m/s[/tex] and [tex]\lambda[/tex] is the wavelength.

So the energy of the electron is,

[tex]E = \dfrac{6.626\times 10^{(-34)} \times 3\times 10^8}{540\times 10^{(-9)}}[/tex]

[tex]E = 3.68 \times 10^{(-19)} \;\rm J[/tex]

The energy of the electron is  [tex]E = 3.68 \times 10^{(-19)} \;\rm J[/tex].

The Emin can be calculated as given below.

[tex]E_{min} = E - KE[/tex]

Where [tex]KE[/tex] is the kinetic energy of the electron that is given as [tex]260 \times 10^{(-20)} \;\rm J.[/tex]

So [tex]E_{min} = 3.68\times 10^{(-19)} - 2.60\times 10^{(-20)}[/tex]

[tex]E_{min} = 36.8\times 10^{(-20)} - 2.60\times 10^{(-20)}[/tex]

[tex]E_{min} = 34.2 \times 10^{(-20)} \;\rm J.[/tex]

The minimum energy of the electron is [tex]E_{min} = 34.2 \times 10^{(-20)} \;\rm J.[/tex]

For the longest wavelength, the electron will have its minimum energy that is Emin.

Hence, the longest wavelength can be calculated as given below.

[tex]\lambda = \dfrac {h\times c} {E_{min}}[/tex]

[tex]\lambda=\dfrac{6.626\times 10^{(-34)} \times 3\times 10^8} {34.2 \times 10^{(-20)}}[/tex]

[tex]\lambda = 549 \times 10^{(-9)} \;\rm m\\\lambda = 549 \;\rm nm[/tex]

The longest wavelength of the electron is 549 nm.

For more details, follow the link given below.

https://brainly.com/question/19634968.