Calculate the De Broglie wavelength of an electron moving with a velocity of [math: 7.26×106ms−1] .Give your answer in standard form to 2 decimal places without units.Example format: [math: 1.23×10−45N] should be written as [ 1.23e-45 ]

Question

BlackTom AI · Accepted Answer

De Broglie wavelength λ = h/p and for a non-relativistic electron p = mv, so λ = h/(m v).

1) Relevant constants and concepts
- Planck’s constant h = 6.62607015 × 10^−34 J·s.
- Electron rest mass m = 9.10938356 × 10^−31 kg.
- Given velocity v = 7.26 × 10^6 m·s^−1.
- Because v ≈ 7.26×10^6 m·s^−1 ≈ 0.024c (c ≈ 3.00×10^8 m·s^−1), the non-relativistic expression p = mv is valid.

2) Step-by-step calculation with intermediate steps
λ = h / (m v)

Compute the denominator m v:
m v = (9.10938356 × 10^−31 kg) × (7.26 × 10^6 m·s^−1)
First multiply the numeric parts: 9.10938356 × 7.26 = 66.134124646
Combine powers of ten: 10^(−31) × 10^6 = 10^(−25)
So m v = 66.134124646 × 10^(−25) kg·m·s^−1 = 6.6134124646 × 10^(−24) (in standard scientific form).

Now divide:
λ = 6.62607015 × 10^(−34) / 6.6134124646 × 10^(−24)
= (6.62607015 / 6.6134124646) × 10^(−34 − (−24))
= 1.001913... × 10^(−10)

3) Rounding and final formatting
Rounded to two decimal places in standard form: 1.00 × 10^(−10).
Following the required input format (no units, "e" notation): 1.00e-10

4) Why this answer is correct
The calculation directly applies the De Broglie relation using accepted physical constants and verifies non-relativistic applicability. The arithmetic yields ≈1.0019e-10 m which correctly rounds to 1.00e-10.

5) Other options
(Not applicable for a single numerical response; any other numeric value differing from 1.00e-10 would contradict the direct calculation above.)

Conclusion: The De Broglie wavelength is 1.00e-10, which matches the provided correct answer.

Calculate the De Broglie wavelength of an electron moving with a velocity of [math: 7.26×106ms−1] .Give your answer in standard form to 2 decimal places without units.Example format: [math: 1.23×10−45N] should be written as [ 1.23e-45 ]数值题

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