Consider an electron (m_e = 9.1 × 10^-31 kg) having energy 13.6 eV, confined in an infinite potential well. If the potential energy inside the well is zero, the expectation value for the square of the electron speed, (v²), is

Concept:

• Average Energy/ Expectation value of energy of an electron is the sum of expectation value of kinetics and potential energy and it is written as

• Also, expectation value of kinetic energy of electron is related to mass of electron (m_e) and the velocity (v) as:

Explanation:

According to the question, the potential energy of the particle/electron inside the well is 0. So, it can be concluded the given energy value is the kinetic energy of the electron

The above relation can be rearranged to get the expectation value of square of velocity as follows:

       ......relation(1)

given,

Equating the values in relation(1), will give:

Conclusion:

Hence, the expectation value of square of velocity of electron confined in the infinite potential well is