Question

Atoms in a solid are in continuous vibrational motion due to thermal energy. At room temperature, the amplitude of these atomic vibrations is typically about 10-9 cm, and their frequency is on the order of 1012 Hz. What is an atom's maximum speed (in m/s)

Answer 1

Answer:

10 m/s

Explanation:

Given:

Amplitude of atomic vibrations (λ) = 10⁻⁹ cm = 10⁻⁹ × 10⁻² m = 10⁻¹¹ m [1 cm = 10⁻² m]

Frequency of the vibrations (f) = 10¹² Hz

In order to find the atom's maximum speed, we need to make use of the formula that relates speed, frequency and wavelength of the vibration.

Therefore, the formula for maximum speed is given as:

$v=f\lambda$

Now, plug in the values given and solve for speed 'v'. This gives,

$v=(10^{12}\ Hz)(10^{-11}\ m)\\\\v=10^{12-11}\ m/s\\v=10\ m/s$

Therefore, the atom's maximum speed due to thermal energy provided is 10 m/s.