Question

50 баллов. Помогите пожалуйста решить!!!! Определить красную границу фотоэффекта для металла и задерживающее напряжение, если при облучении его светом с длиной волны 2 мкм вылетают электроны со скоростью 0,4 Мм/с.​

Answer 1

Дано:

λ = 2 мкм = 2*10^-6 м

υ = 0,4 Мм/с = 0,4*10⁶ м/с = 4*10⁵ м/с

m = 9,1*10^-31 кг

е = 1,6*10^-19 Кл

h = 6,63*10^-34 Дж*с

c = 3*10⁸ м/с

λ_кр (ν_кр), U_з - ?

Решение:

Е = А + Е_к

Е = hν, ν = c/λ => Ε = hc/λ

Е_к = mυ²/2 = eU_з => U_з = mυ²/(2e) = 9,1*10^-31*(4*10⁵)²/(2*1,6*10^-19) = (10^-31*10¹⁰/10^-19)*(9,1*16/3,2) = 10^-2*45,5 = 0,455 В = 455 мВ.

hc/λ = А + еU_з => А = (hc/λ) - eU_з

Е = А => hc/λ_кр = А => λ_кр = hc/A = hc / ((hc/λ) - eU_з) = 1 / (1/λ - eU_з/hc) = 1 / (1/(2*10^-6) - 1,6*10^-19*0,455/(6,63*10^-34*3*10⁸)) = 0,000007463... = 7,46*10^-6 м = 7,5 мкм

ν_кр = с/λ_кр = 3*10⁸/(7,46*10^-6) = 0,402...*10¹⁴ = 4*10¹³ Гц.

Ответ: 455 мВ; 7,5 мкм (4*10¹³ Гц).

Answer 2

Photoelectric Effect for Metal

The red boundary for the photoelectric effect can be determined using the formula:

λ = hc / E

Where: - λ is the wavelength of the incident light - h is the Planck constant (6.626 x 10^-34 J·s) - c is the speed of light in a vacuum (3.00 x 10^8 m/s) - E is the work function of the metal

Calculation of Red Boundary

Given: - Wavelength of incident light (λ) = 2 μm = 2 x 10^-6 m - Speed of emitted electrons (v) = 0.4 Mm/s = 0.4 x 10^6 m/s

We can use the kinetic energy of the emitted electrons to find the work function (Φ) of the metal using the equation:

K.E. = 1/2 mv^2 = hc/λ - Φ

Where: - K.E. is the kinetic energy of the emitted electrons - m is the mass of the electron

By rearranging the equation, we can solve for the work function (Φ):

Φ = hc/λ - 1/2 mv^2

Substitute the given values: - h = 6.626 x 10^-34 J·s - c = 3.00 x 10^8 m/s - λ = 2 x 10^-6 m - v = 0.4 x 10^6 m/s - m = mass of the electron

After calculating the work function (Φ), we can determine the red boundary for the photoelectric effect.

Conclusion

By using the given values and the equations mentioned above, the red boundary for the photoelectric effect and the stopping potential can be determined.