Q. 44.3( 27 Votes )

# Monochromatic lig

Answer :

(a) Energy of photon E = hv = hc/λ

Where h = plank’s constant = 6.63 × 10^{-34} J. sec

ν = max. frequency of X-ray

c = speed of light = 3 × 10^{8} m/s

λ = minimum wavelength of X-ray

E = 6.63 × 10^{-34} × 3 × 10^{8} / 632.8 x10^{-9}

∴ E = 3.14 × 10^{-19} J

Now, p = h / λ

p = momentum of photon

p = 6.63 × 10^{-34}/632.8 x10^{-9}

∴ p = 1.05 × 10^{-27} kg-m/sec

__Maximum energy and momentum of the electron are 3.14 × 10 ^{-19} J and 1.05 × 10^{-27} kg-m/sec respectively.__

(b) No. of photons ‘n’ per sec. is equal to total power radiated divided by number of photons (it is assumed that power of each and every photon is same and all the photons are falling on the target).

‘n’ = P/E

Where P = radiated power of LASSER

n = 9.42 × 10^{6}/3.14 × 10^{-19}

n = 3 × 10^{16} photons/sec.

__No. of photons falling per second is equal to 3 × 10 ^{16} photons/sec.__

(c) mv = p

m = mass of Hydrogen = mass of proton = 1.67 × 10^{-27} kg

v = speed of Hydrogen

p = momentum of photon as well as Hydrogen atom

v = p/m

v = 1.05 × 10^{-27}/1.67 × 10^{-27} = 0.63 m/sec.

__Required speed of Hydrogen atom is 0.63 m/sec.__

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