Question

A beam of electrons (m = 9.11 × 10-31 kg/electron) has an average speed of 1.9 × 108 m/s. What is the wavelength of electrons having this average speed, in picometers?

Answer 1

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