Q1
The de-Broglie wavelength for a He atom travelling at 1000 m/s (typical speed at room temperature) is
A.
99.7 × 10-12 m
AnswerB.
199.4 × 10-12 m
C.
199.4 × 10-18 m
D.
99 × 10-6 m
Answer: Option A
Solution
Answer: Option A
Solution:
This question is about the de Broglie wavelength, which tells us that even particles like atoms can behave like waves! The de Broglie wavelength (λ) is calculated using the formula: λ = h/mv
where:
h is Planck's constant (6.626 x 10-34 Js)
m is the mass of the particle (in kg)
v is the velocity of the particle (in m/s)
First, we need the mass of a Helium (He) atom. A He atom has a mass of approximately 4 amu (atomic mass units). To use the formula, we need to convert this to kilograms. Since 1 amu ≈ 1.66 x 10-27 kg, the mass of a He atom is roughly 4 * 1.66 x 10-27 kg = 6.64 x 10-27 kg.
Now, we can plug the values into the de Broglie wavelength formula:
λ = (6.626 x 10-34 Js) / (6.64 x 10-27 kg * 1000 m/s)
After calculating, you will get a wavelength around 99.7 x 10-12 m.