For photoelectric emission from a certain metal, the threshold frequency is n. When radiation of frequency 2n strikes the metal surface, what is the maximum speed of the emitted photoelectrons? (m = mass of electron)

2 * sqrt(h * n / m)
sqrt(h * n / (2 * m))
sqrt(h * n / m)
sqrt(2 * h * n / m)

Correct answer: sqrt(2 * h * n / m)

Solution

Using Einstein's photoelectric equation: h * nu = phi + (1/2) * m * v². Here phi = h * n and nu = 2n, so (1/2) * m * v² = h * (2n) - h * n = h * n. Therefore v = sqrt(2 * h * n / m).

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