Frequency of Einstein at 240 Kelvin

To answer this question, we need to understand what Einstein frequency means and how it relates to temperature.

What is Einstein frequency?
Einstein frequency is the quantum mechanical property of a material that describes how fast its atoms or molecules vibrate. It is related to the energy of the material, and it can be calculated using the Einstein model of solids.

How does it relate to temperature?
As we increase the temperature of a material, its atoms or molecules start to vibrate faster, which leads to an increase in its Einstein frequency. This is because the energy of the material increases with temperature, and the frequency is directly proportional to the energy.

Now, to calculate the Einstein frequency at 240 Kelvin, we need to know the energy of the material at that temperature. We can use the following formula to calculate it:

E = kT

where E is the energy, k is the Boltzmann constant, and T is the temperature in Kelvin.

Once we know the energy, we can use the following formula to calculate the Einstein frequency:

v = (E/h)^(1/2)

where v is the Einstein frequency, E is the energy, and h is the Planck constant.

Putting it all together, we get:

E = kT = (1.380649 × 10^-23 J/K) × (240 K) = 3.3135576 × 10^-21 J

v = (E/h)^(1/2) = [(3.3135576 × 10^-21 J)/(6.62607015 × 10^-34 J·s)]^(1/2) = 6.676 × 10^11 Hz

Therefore, the Einstein frequency at 240 Kelvin is approximately 6.676 × 10^11 Hz.