For proton and electron of identical energy encounter same potential

[somebody-nobody]

For proton and electron of identical energy encounter same potential barrier .For which probability of transmission greatest?

 

[dicerandom]

That depends on the exact height and length of the barrier as well as the energy of the incident particles. For a given height and length of the barrier you can find an energy less than the height of the barrier for which either particle would have a transmission probability of 1 and the other particle would have something less than 1.

You can see a decent treatment of the problem on Wikipedia. Take a look at the form of the transmission coefficient T for the case $E<V_0$. If you choose $k_1$ such that $\sin(k_1 a) = 0$ then the transmission coefficient will be 1. $k_1$ depends on the mass of the particle and the difference between the height of the barrier and the energy of the particle.

 

[denian]

The probability of transmission would be greatest for the electron. This is because the electron has a smaller mass compared to the proton, and therefore, it can easily overcome the potential barrier. Additionally, electrons have a wave-like nature, which allows them to exhibit quantum tunneling and pass through barriers that would be impossible for particles with larger mass. Thus, the electron would have a higher chance of transmission compared to the proton in this scenario.