Question

Platinum has a work function (also called binding energy) of 9.05 × 10-19 J. Which is the longest wavelength that could cause emission of electrons? 2.196 × 106 m 5.654 × 102 m 2.196 × 10-7 m 1.37 × 1015 m 4.553 × 10-6 m

Answer 1

2,196 10⁻⁷ m

Step-by-step explanation:

This is a problem of photoelectric effect, which was explained by Einstein, assuming that the light was formed by quanta of energy that collide with the electors and is described by the expression

`K_(max)` = h f -Ф

Where
`K_(max)` is the maximum kinetic energy of the expelled electrons h is the Planck constant that is worth 6,626 10-34 J s, f is the radiation frequency and Ф is the material's work function.

For the wavelength of greater wavelength (lower energy) the kinetic energy of the electors must decrease to a minimum of zero.

0 = hf -Ф

hf = Ф

f = Ф / h

f = 9.05 10-19 / 6,626 10-34

f = 1,366 10 15 Hz

Now the speed of the wave is related to the wavelength and frequency

c = λ f

λ = c / f

λ = 3 10⁸ / 1,366 10¹⁵

λ = 2,196 10⁻⁷ m

The result is 2,196 10⁻⁷ m