### Areas Dominador Tan is Knowledgeable in:

Chemistry, Physics, Statistics, and Biology

### Techniques Dominador Tan Uses:

Identify the problem that needs to be solved. One of the easiest ways to identify a problem is to ask questions

### Dominador Tan's Problem Solving Experience:

- By how much does the tunneling current through the tip of an STM change if the tip rises 0.020 nm from some initial height above a sodium surface with a work function W0=2.28eV? [Hint: Let the work function (see Section 37-2) equal the energy needed to raise the electron to the top of the barrier.]

Solution:

In this problem, we are given a scanning tunneling microscope for which we want to estimate the change of the tunneling current if the tip of the microscope moves away for 0.020 from the sodium surface.

T1= Ae^-2GI

and

T2= Ae^-2G (l + deltal)

Next, drop in transmission which is going to be defined as,

T2/T1= Ae^-2G(l + deltal)/ Ae^-2GI= e^-2Gdelta l

Next, Calculate the exponent:

exp= 2 x 0.0x10^-9 x squareroot 2 x 9.11x10^-31 x 2.28 x 1.6x10^-19/ h

exp= -0.3091

Finally, get the ratio between tunneling current:

T2/T1= e^-2Gdeltal= e^-0.3091

T2/T1= 0.73

Therefore, the current drops for about 27%.