Yes, quantum tunneling can occur through different materials at different rates. The probability of quantum tunneling depends on various factors, including the properties of the material involved.
Quantum tunneling is a phenomenon in which particles can pass through potential energy barriers that would be classically impossible to overcome. It arises from the wave-like nature of particles, as described by quantum mechanics. When a particle encounters a potential barrier, there is a finite probability that it will tunnel through and appear on the other side.
The rate of quantum tunneling depends on several factors, such as the width and height of the barrier, the mass of the particle, and the particle's energy. Additionally, the properties of the material through which the tunneling occurs can influence the tunneling rate.
In the case of different materials, their electronic structure and atomic properties play a significant role. The density, atomic spacing, and electronic configuration of a material can affect the tunneling probability. Materials with higher atomic densities or stronger bonding may present higher potential energy barriers, making tunneling less likely.
In your example, lead and beryllium have different atomic structures and densities. Lead has a higher density and a more complex atomic arrangement compared to beryllium. Consequently, tunneling through lead may generally occur less frequently than through beryllium, assuming all other factors remain constant.
However, it's important to note that the tunneling phenomenon is highly dependent on specific conditions, such as the energy of the particle and the particular configuration of the potential barrier. Therefore, while certain materials may exhibit higher or lower tunneling rates on average, it is possible to engineer and manipulate materials to enhance or suppress quantum tunneling effects.