Question

The potential energy difference between the tip of an electron scanning microscope and the surface is...

  1. The potential energy difference between the tip of an electron scanning microscope and the surface is 2.09x10-18 J. The energy of an electron is 1.02x10-18 J. What length must the tip be from the surface for the probability of an electron tunneling from the tip to the surface is 0.75?

Homework Answers

Answer #1

The probability of tunneling T is given by:

T = exp ( - 2GL)

which on rearranging gives:

L = - ln(T) / 2G

where ;

L = tunneling length

T = tunneling probability = 0.75

G = ( 2m (U - E) / h^2 )^0.5

where;

m = mass of electron = 9.1 X 10^-31 kg

U = potential energy barrier = 2.09 X 10^-18 J

E = energy of electron = 1.02 X 10^-18 J

h = reduced Planck's constant = 1.05 X 10^-34 J / s

Therefore;

G =  ( 2 X 9.1 X 10^-31 X (2.09 X 10^-18 - 1.02 X 10^-18) / (1.05 X 10^-34)^2 )^0.5

which gives;

G = 1.33 X 10^8

Substituting this in the equation;

L = - ln(T) / 2G

L = - ln(0.75) / ( 2 X 1.33 X 10^8)

L = 1.082 X 10^-9 m

L = 1.082 nm

which is the required length the tip must be from the surface.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
What are the SIMILARITIES and DIFFERENCES between Scanning Electron Microscope (SEM) and Scanning Tunneling Microscope?
What are the SIMILARITIES and DIFFERENCES between Scanning Electron Microscope (SEM) and Scanning Tunneling Microscope?
Explain the SIMILARITIES and DIFFERENCES between Scanning Electron Microscope (SEM) and Scanning Tunneling Microscope?
Explain the SIMILARITIES and DIFFERENCES between Scanning Electron Microscope (SEM) and Scanning Tunneling Microscope?
The design criterion for a typical scanning tunneling microscope (STM) specifies that it must be able...
The design criterion for a typical scanning tunneling microscope (STM) specifies that it must be able to detect, on the sample below its tip, surface features that differ in height by only 0.004 90 nm. Assuming the electron transmission coefficient is e?2CL   with C = 10.0 nm?1, what percentage change in electron transmission must the electronics of the STM be able to detect to achieve this resolution?
a) In an electron microscope, a potential difference of 20 kV is applied to accelerate the...
a) In an electron microscope, a potential difference of 20 kV is applied to accelerate the electrons. Determine the wavelength (in m) of the X-ray photons of equal energy as said electrons. If the wavelength of the X-rays is between 10 and 0.01 nm, what can you deduce about its calculation? b) An electron and a neutron have the same wavelength of de Broglie.
For electron microscope which accelerates electrons from rest through a potential difference of 10 kV. (a)...
For electron microscope which accelerates electrons from rest through a potential difference of 10 kV. (a) If the potential energy of an electron is taken to be 0 initially (at a 0 V plate), what potential energy does it have in Joules after accelerating to the 10 kV plate? (The electrons actually pass through a small hole in this plate before continuing on toward the sample). (b) What speed does the electron reach by the time it reaches the 10...
An electron having total energy E = 3.40 eV approaches a rectangular energy barrier with U...
An electron having total energy E = 3.40 eV approaches a rectangular energy barrier with U = 4.10 eV and L = 950 pm as shown in the figure below. Classically, the electron cannot pass through the barrier because E < U. Quantum-mechanically, however, the probability of tunneling is not zero. (a) Calculate this probability, which is the transmission coefficient. (Use 9.11  10-31 kg for the mass of an electron, 1.055  10-34 J · s for ℏ, and note that there are...
The electron microscope can "see" smaller detail than an optical microscope because the wavelength of the...
The electron microscope can "see" smaller detail than an optical microscope because the wavelength of the electron can be made much shorter than visible light. Now consider the possibility of a proton microscope. By what potential difference (in volts) must A) a proton and B) an electron be accelerated to give a wavelength of 5x10-12m? Can you think of a reason why we have electron microscopes, but do not commonly have proton microscopes?
(a) Calculate the gravitational potential energy of a 78 kg mass on the surface of the...
(a) Calculate the gravitational potential energy of a 78 kg mass on the surface of the Earth._____ J (b) Calculate the gravitational potential energy at an altitude of 3 km._____J (c) Take the difference between the results for parts (b) and (a), and then compare this with mgh, where h = 3 km. _____J (difference between parts a and b) _____J (difference between a and b) / (mgh)
An electron microscope accelerates electrons from rest through a potential difference of 10 kV. The charge...
An electron microscope accelerates electrons from rest through a potential difference of 10 kV. The charge on an electron is -1.60×10-19C and the mass of an electron is 9.11×10-31kg. (a) If the potential energy of an electron is taken to be 0 initially (at a 0 V plate), what potential energy does it have in Joules after accelerating to the 10 kV plate? (The electrons actually pass through a small hole in this plate before continuing on toward the sample)....
If the minimum energy (work function) required to eject an electron from a copper surface by...
If the minimum energy (work function) required to eject an electron from a copper surface by the photoelectric effect is 7.81 ✕ 10^−19 J, what is the wavelength (in nanometers) of a photon of that energy?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT