Question

Максимальна кінетична енергія електронів, які вилітають з рубідію при його освітленні ультрафіолетовими променями з довжиною хвилі 317 на, дорівнює 2,84*10^-19 Дж. Визначити роботу виходу електронів з рубідію і червону межу фотоефекта

Answer 1

Решение закреплено ниже:

Answer 2

Calculation of Maximum Kinetic Energy of Electrons

To calculate the maximum kinetic energy of electrons emitted from rubidium when illuminated with ultraviolet light of wavelength 317 nm, we can use the equation for the energy of a photon:

E = hc/λ

where: - E is the energy of the photon - h is Planck's constant (6.626 x 10^-34 J·s) - c is the speed of light (3.00 x 10^8 m/s) - λ is the wavelength of the light

Given that the maximum kinetic energy of the electrons is 2.84 x 10^-19 J and the wavelength of the ultraviolet light is 317 nm (or 317 x 10^-9 m), we can rearrange the equation to solve for the work function (Φ) of rubidium:

Φ = E - hc/λ

Substituting the values into the equation:

Φ = (2.84 x 10^-19 J) - [(6.626 x 10^-34 J·s) x (3.00 x 10^8 m/s) / (317 x 10^-9 m)]

Calculating the value:

Φ ≈ 2.84 x 10^-19 J - 6.24 x 10^-19 J

Φ ≈ -3.40 x 10^-19 J

The negative sign indicates that the work function is the amount of energy required to remove an electron from the material. In this case, the work function of rubidium is approximately 3.40 x 10^-19 J.

Red Threshold of the Photoelectric Effect

The red threshold, also known as the threshold frequency or threshold wavelength, refers to the minimum frequency or wavelength of light required to cause the photoelectric effect. When light with a frequency or wavelength below the threshold is incident on a material, no electrons are emitted regardless of the intensity of the light.

To determine the red threshold or the minimum wavelength of light for the photoelectric effect, we can use the equation:

E = hf

where: - E is the energy of the photon - h is Planck's constant (6.626 x 10^-34 J·s) - f is the frequency of the light

Since we are given the wavelength of the ultraviolet light (317 nm), we can calculate the frequency (f) using the speed of light equation:

c = λf

where: - c is the speed of light (3.00 x 10^8 m/s) - λ is the wavelength of the light

Rearranging the equation to solve for f:

f = c/λ

Substituting the values:

f = (3.00 x 10^8 m/s) / (317 x 10^-9 m)

Calculating the value:

f ≈ 9.46 x 10^14 Hz

Now, we can calculate the red threshold wavelength by rearranging the energy equation:

E = hf

λ = c/f

λ = (3.00 x 10^8 m/s) / (9.46 x 10^14 Hz)

Calculating the value:

λ ≈ 3.18 x 10^-7 m

Therefore, the red threshold wavelength for the photoelectric effect is approximately 318 nm.