Question

Determine the deBroglie wavelength for an electron moving at 7.3 x 107 m/sec.

A. 1.0 x 10-11 m

B. 5.1 x 104 m

C. 5.9 x 10-23 m

D. 2.9 x 10-7 m

Answer 1

A.
`\lambda_(db) = 1.0 * 10^(-11) m`

Step-by-step explanation:

As we know that de Broglie wavelength is given by the formula

`\lambda_(db) = (h)/(mv)`

here we know that

`h = 6.6 * 10^(-34)`

mass of electron is given as

`m = 9.1 * 10^(-34) kg`

`v = 7.3 * 10^7 m/s`

so here we have

`\lambda_(db) = (6.6 * 10^(-34))/((9.1 * 10^(-31))(7.3 * 10^7))`

`\lambda_(db) = 0.99 * 10^(-11) m`

`\lambda_(db) = 1.0 * 10^(-11) m`

Answer 2

Wavelength is obtained by Planck’s constant over the product of mass and velocity.

w = h / mv

w =wavelength
h = Planck’s constant = 6.626 x 10^-34
m = mass (kg) = 9.11 x 10^-31
v = velocity = 7.3 x 10^7 m/sec

Substitute all the given to the formula.
w = 6.626 x 10^-34 / (9.11 x 10^-31)(7.3 x 10^7)

w = 0.00996 nm ≈ 1 x 10^-11 m

The answer is A