Atomic Structure: JEE Main Chemistry Question with Solution
The wavelength of an electron of kinetic energy 4.50×10−29J is...... ×10−5 m. (Nearest integer)
Given : mass of electron is 9×10−31 kg, h=6.6×10−34 J s
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Hint 1 of 3
Which formula directly relates the de Broglie wavelength (λ) to the kinetic energy (K) and mass (m) of a particle?
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Correct answer
The de Broglie wavelength of the electron is approximately 7 × 10⁻⁵ m, so the required value is 7.
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Solution
StepWorking
01given
Kinetic energy KE=4.50×10−29 J, mass of electron m=9×10−31 kg, Planck's constant h=6.6×10−34 J s.
02strategise
Use the de Broglie relation expressed in terms of kinetic energy: λ=ph=2m(KE)h.
03execute
Substitute the given numerical values into the formula:
λ=2×(9×10−31)×(4.50×10−29)6.6×10−34
Inside the radical:
2×9×4.50×10−60=81×10−60
Taking square root:
81×10−60=9×10−30 kg m/s
Now computing λ:
λ=9×10−306.6×10−34=96.6×10−4=0.733×10−4=7.33×10−5 m
Reporting in units of 10−5 m to the nearest integer gives 7.
✓verify
7.33×10−5 m rounded to the nearest integer is 7. Order of magnitude is consistent with low kinetic energy.
Hints that build this answer step by step
Which formula directly relates the de Broglie wavelength (λ) to the kinetic energy (K) and mass (m) of a particle?
λ = h / √(2mK)
What is the momentum (p = √(2mK)) of the electron given m = 9 × 10⁻³¹ kg and K = 4.50 × 10⁻²⁹ J?
9.0 × 10⁻³⁰ kg m s⁻¹
Substituting h = 6.6 × 10⁻³⁴ J s and p = 9.0 × 10⁻³⁰ kg m s⁻¹ into λ = h / p, what is the wavelength expressed as [value] × 10⁻⁵ m rounded to the nearest integer?