A metal with a 500 nm red border of the photoelectric effect is illuminated by radiation with a frequency of 7.5 x 10 ^ 14 Hz.

| March 9, 2021 | education

A metal with a 500 nm red border of the photoelectric effect is illuminated by radiation with a frequency of 7.5 x 10 ^ 14 Hz. What can be the maximum speed of photoelectrons?

λcr = 500 nm = 500 * 10 ^ -9 m.

v = 7.5 * 10 ^ 14 Hz.

h = 6.6 * 10 ^ -34 J * s.

m = 9.1 * 10 ^ -31 kg.

C = 3 * 10 ^ 8 m / s.

Vmax -?

The energy of the incident photons Eph goes to knocking out electrons from the surface of the metal Av and imparting kinetic energy Ek to them: Ef = Av + ​​Ek – the law of the photoelectric effect.

The energy of photons Eph is expressed by the formula: Eph = h * v, where h is Planck’s constant, v is the frequency of the incident light.

Eph = 6.6 * 10 ^ -34 J * s * 7.5 * 10 ^ 14 Hz = 50193 * 10 ^ -34 J.

We express the work function of Av to pull out electrons from the metal surface by the formula: Av = h * C / λcr, where λcr is the red border of the photoelectric effect.

Av = 6.6 * 10 ^ -34 J * s * 3 * 10 ^ 8 m / s / 500 * 10 ^ -9 m = 3.96 * 10 ^ -19 J.

As you can see, the energy of light Eph is not enough even to snatch an electron from the surface of the metal Av.

Answer: under the given conditions of the problem, the phenomenon of the photoelectric effect will not be observed, electrons will not fly out from the surface of the metal Vmax = 0 m / s.



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