White light (ranging in wavelengths from 380 to 750 nm) is incident on a metal with...

White light (ranging in wavelengths from 380 to 750 nm) is incident on a metal with work function W_o = 2.68 eV.

1. For what range of wavelengths (from l_min to l_max) will NO electrons be emitted?

a) Imin=

b) Imax=

Solutions

Expert Solution

Einstein's Photoelectric equation, explain that a part of energy of photon ( hv) is used in liberating the electron from metal surface which is equal to work function (@₀ ) .Rest part of energy of photon providing maximum kinetic energy ( 1/2*m*v^{2 )} to photon. It is given as:

hv = @₀ + 1/2*m*v_²max

hv ( frequency) = Energy of photon, @₀ = work function. K.E = 1/2*m*v²

Electron emission will stop when bombarding photon has energy less than the work function.

So @₀ = hv

v = @₀ / h

v = 2.68*1.6*10^-19 J / 6.63*10^-34 J-s

v = 6.467*10¹⁴ hz

From , c = v*lambda ( by velocity ( c) = frequency (v) *wavelength (lambda) )

lambda = c / v

= 3*10⁸ / 6.467*10¹⁴ = 463.8 nm

This refers to lmin = 463 nm where electron leaves with zero K.E

At any wavelength less than 463 nm no electron will be emitted.

Maximun wavelength = 750 nm is given in Q.

so No electron emission with lambda between 463 nm- 750 nm

lmin = 463 nm

lmax = 750nm

genius_generous answered 1 month ago

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