Consider a 1D rectangular potential barrier extends from 0 to a and has a height of...

Transcribed Image Text:

Consider a 1D rectangular potential barrier extends from 0 to a and has a height of V > E and has an incoming particle from the left side of the barrier. a. Verify that the accurate transmission equation reduces to the simple version when the barrier is very high and wide. b. Use the simple transmission probability equation to predict the tunneling probability produced by an STM tip that is 1 away from a metal surface. Note that the tunneling particle is an electron (m=me) and a typical barrier height is V=5 eV. Assume that the electrons have a typical energy E = K Boltzmann T where T = 300 K due to the thermal energy, which is ultimately equivalent to E = 1 eV, and thus V - E V. **Hint** Check all units. 40 = 1 40 c. Use the simple transmission probability equation to predict the tunneling probability of a proton with thermal energy of E eV when it encounters a barrier of height V=2E and a width of 1 as is typically the case for proton tunneling in a hydrogen bonded system. Consider a 1D rectangular potential barrier extends from 0 to a and has a height of V > E and has an incoming particle from the left side of the barrier. a. Verify that the accurate transmission equation reduces to the simple version when the barrier is very high and wide. b. Use the simple transmission probability equation to predict the tunneling probability produced by an STM tip that is 1 away from a metal surface. Note that the tunneling particle is an electron (m=me) and a typical barrier height is V=5 eV. Assume that the electrons have a typical energy E = K Boltzmann T where T = 300 K due to the thermal energy, which is ultimately equivalent to E = 1 eV, and thus V - E V. **Hint** Check all units. 40 = 1 40 c. Use the simple transmission probability equation to predict the tunneling probability of a proton with thermal energy of E eV when it encounters a barrier of height V=2E and a width of 1 as is typically the case for proton tunneling in a hydrogen bonded system.