11.16 An electron and a photon each have a wavelength of 1.00 nm. Find
(a) Their momentum,
(b) The energy of the photon, and
(c) The kinetic energy of electron.
11.16 An electron and a photon each have a wavelength of 1.00 nm. Find
(a) Their momentum,
(b) The energy of the photon, and
(c) The kinetic energy of electron.
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1 Answer
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11.16 Wavelength of electron, = Wavelength of proton, = 1.0 nm = 1 m
Planck’s constant, h = 6.626 Js
From De Broglie wavelength relation, where p = momentum
= = = 6.626 kg.m/s. Since , their momentum will be also equal.
The energy of photon is given by the relation: =
where c = speed of light = 3 m/s
= Js = eV = 1242.38 eV = 1.242 keV
Kinetic energy of electron, having momentum p is given by the relation
= where m = mass of electron = 9.1 kg.
Hence,&nbs
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Based on theory
z² × (13.6) (1 - ¼) = 3 × (13.6)
z = 2 . (i)
h/√2mk? = (1/2.3) × h/√2mk?
=> k? = (2.3)²k? = 5.25k? (ii)
Now, k? = E? - Φ
k? = E? - Φ = z²E? - Φ
∴ k? /k? = (10.2 - Φ)/ (4 × 10.2 - Φ) = 1/5.25
=> Φ = 3eV
- (i)
- (ii)
from (i) & (ii)
ev
hu = hu0 + K.E
Cases u = 2u0
h2u0 = hu0 + K.E1
K.E1 = hu0
- (1)
Now, cases 2
h 5u0 = hu0 + k.E2
k.E2 = 4hu0
v2 =
v2 = 2v1
This is a Short Answer Type Questions as classified in NCERT Exemplar
Sol:
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