Answer :
Answer:
12 pm
Explanation:
Step 1: Given data
- Mass of an electron (m): 9.11 × 10⁻³¹ kg
- Average speed of an electron (v): 1.9 × 10⁸ m/s
- Speed of light (c): 3.00 × 10⁸ m/s
- Planck's constant (h): 6.63 × 10⁻³⁴ J.s
- Wavelength of an electron (λ): ?
Step 2: Calculate the kinetic energy (E) of an electron
We will use the following expression.
E = 1/2 × m × v²
E = 1/2 × 9.11 × 10⁻³¹ kg × (1.9 × 10⁸ m/s)²
E = 1.6 × 10⁻¹⁴ J
Step 3: Calculate the wavelength of an electron
We will use the following expression.
E = h × c / λ
λ = h × c / E
λ = 6.63 × 10⁻³⁴ J.s × 3.00 × 10⁸ m/s / 1.6 × 10⁻¹⁴ J
λ = 1.2 × 10⁻¹¹ m
Step 4: Convert "λ" to picometers
We will use the relationship 1 m = 10¹² pm.
1.2 × 10⁻¹¹ m × (10¹² pm/1 m) = 12 pm
The wavelength of the beam of electrons is 3.8 pm.
Using the De Broglie relation;
λ = h/mv
λ = wavelength
h = Plank's constant
m = mass of the object
v = speed of the object
Now;
λ = ?
h = 6.6 × 10^-34 Js
m = 9.11 × 10^-31 kg
v = 1.9 × 10^8 m/s
So;
λ = 6.6 × 10^-34 Js/ 9.11 × 10^-31 kg × 1.9 × 10^8 m/s
λ = 6.6 × 10^-34 /1.73 × 10^-22
λ = 3.8 × 10^- 12 m or 3.8 pm
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