To find:
The wavelengths of the given objects.
Answer to Problem 3.67QA
Solution:
a) 10.8 nm
b) 0.180 nm
c) 8.2 x 10-28 nm
d) 3.7 x 10-54 nm
Explanation of Solution
1) Concept:
According to De Broglie,
All material particles in motion possess wave characteristics.
So, according to him, the wave-length associated with a particle of mass ‘m’ and moving with a velocity ‘v’ is given by the relation,
λ =
2) Formula:
λ =
3) Calculations:
(a)
Mass of muon = 1.884 x 10-28 kg,
velocity = 325 m/s,
h (Planck’s Constant) = 6.626 x 10-34 J.s.
So wavelength (λ) =
(b)
Mass of electron = 9.10938 x 10-31 kg,
velocity = 4.05 x 106 m/s,
h (Planck’s Constant) = 6.626 x 10-34 J.
So wavelength (λ) =
(c)
Mass of sprinter = 82 kg,
velocity =9.9 m/s,
h (Planck’s Constant) = 6.626 x 10-34 J.s
So wavelength (λ) =
(d)
Mass of earth =6 x 1024 kg,
velocity =3 x 104 m/s,
h (Planck’s Constant) = 6.626 x 10-34 J.s
So wavelength (λ) =
Conclusion:
Therefore the respective wavelengths for (a),(b),(c) and (d) are 10.8 nm, 0.18 nm, 8.2 x 10-28 nm and 3.7 x 10-54 nm.
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