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What is the fraction of a beam of electrons, each of energy E = 0.08 eV reflected from a step barrier of height V0 = 0.06 eV and of infinite width?
- a)0.11
- b)0.33
- c)0.67
- d)0.89
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
What is the fraction of a beam of electrons, each of energy E = 0.08 e...
The fraction of beam reflected from the step barrier on width 
is given as
Here , E = 0.08 eV
V = 0.06 eV
⇒ E - V0 = 0.02 eV
So, fraction of reflected beam
is given asHere , E = 0.08 eV
V = 0.06 eV
⇒ E - V0 = 0.02 eV
So, fraction of reflected beam
This question is part of UPSC exam. View all Physics courses
Most Upvoted Answer
What is the fraction of a beam of electrons, each of energy E = 0.08 e...
Reflection of Electrons from a Step Barrier
Given:
Energy of electrons, E = 0.08 eV
Height of the step barrier, V0 = 0.06 eV
To find:
Fraction of electrons reflected from the step barrier
Formula:
The reflection coefficient for electrons can be calculated using the formula:
R = |(k2 - k1)/(k2 + k1)|^2
Where:
k1 = sqrt(2mE)/ħ (wavevector of incident electrons)
k2 = sqrt(2m(E - V0))/ħ (wavevector of reflected electrons)
m = mass of electron
ħ = reduced Planck's constant
Calculation:
1. Calculate the wavevectors:
k1 = sqrt(2mE)/ħ
k2 = sqrt(2m(E - V0))/ħ
2. Substitute the given values:
m = mass of electron = 9.11 x 10^-31 kg
E = 0.08 eV = 0.08 x 1.6 x 10^-19 J (converting eV to Joules)
V0 = 0.06 eV = 0.06 x 1.6 x 10^-19 J (converting eV to Joules)
ħ = 6.63 x 10^-34 J.s (reduced Planck's constant)
3. Calculate the wavevectors using the given formula:
k1 = sqrt(2mE)/ħ
k2 = sqrt(2m(E - V0))/ħ
Substitute the values and calculate k1 and k2.
4. Calculate the reflection coefficient:
R = |(k2 - k1)/(k2 + k1)|^2
Substitute the calculated values of k1 and k2 in the formula and calculate the reflection coefficient.
5. The fraction of electrons reflected is equal to the square of the reflection coefficient:
Fraction reflected = R^2
Substitute the calculated value of R in the formula and calculate the fraction of electrons reflected.
Answer:
The correct answer is option 'B' (0.33).
Given:
Energy of electrons, E = 0.08 eV
Height of the step barrier, V0 = 0.06 eV
To find:
Fraction of electrons reflected from the step barrier
Formula:
The reflection coefficient for electrons can be calculated using the formula:
R = |(k2 - k1)/(k2 + k1)|^2
Where:
k1 = sqrt(2mE)/ħ (wavevector of incident electrons)
k2 = sqrt(2m(E - V0))/ħ (wavevector of reflected electrons)
m = mass of electron
ħ = reduced Planck's constant
Calculation:
1. Calculate the wavevectors:
k1 = sqrt(2mE)/ħ
k2 = sqrt(2m(E - V0))/ħ
2. Substitute the given values:
m = mass of electron = 9.11 x 10^-31 kg
E = 0.08 eV = 0.08 x 1.6 x 10^-19 J (converting eV to Joules)
V0 = 0.06 eV = 0.06 x 1.6 x 10^-19 J (converting eV to Joules)
ħ = 6.63 x 10^-34 J.s (reduced Planck's constant)
3. Calculate the wavevectors using the given formula:
k1 = sqrt(2mE)/ħ
k2 = sqrt(2m(E - V0))/ħ
Substitute the values and calculate k1 and k2.
4. Calculate the reflection coefficient:
R = |(k2 - k1)/(k2 + k1)|^2
Substitute the calculated values of k1 and k2 in the formula and calculate the reflection coefficient.
5. The fraction of electrons reflected is equal to the square of the reflection coefficient:
Fraction reflected = R^2
Substitute the calculated value of R in the formula and calculate the fraction of electrons reflected.
Answer:
The correct answer is option 'B' (0.33).
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What is the fraction of a beam of electrons, each of energy E = 0.08 eV reflected from a step barrier of height V0 = 0.06 eV and of infinite width?a)0.11b)0.33c)0.67d)0.89Correct answer is option 'B'. Can you explain this answer?
Question Description
What is the fraction of a beam of electrons, each of energy E = 0.08 eV reflected from a step barrier of height V0 = 0.06 eV and of infinite width?a)0.11b)0.33c)0.67d)0.89Correct answer is option 'B'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about What is the fraction of a beam of electrons, each of energy E = 0.08 eV reflected from a step barrier of height V0 = 0.06 eV and of infinite width?a)0.11b)0.33c)0.67d)0.89Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the fraction of a beam of electrons, each of energy E = 0.08 eV reflected from a step barrier of height V0 = 0.06 eV and of infinite width?a)0.11b)0.33c)0.67d)0.89Correct answer is option 'B'. Can you explain this answer?.
What is the fraction of a beam of electrons, each of energy E = 0.08 eV reflected from a step barrier of height V0 = 0.06 eV and of infinite width?a)0.11b)0.33c)0.67d)0.89Correct answer is option 'B'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about What is the fraction of a beam of electrons, each of energy E = 0.08 eV reflected from a step barrier of height V0 = 0.06 eV and of infinite width?a)0.11b)0.33c)0.67d)0.89Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the fraction of a beam of electrons, each of energy E = 0.08 eV reflected from a step barrier of height V0 = 0.06 eV and of infinite width?a)0.11b)0.33c)0.67d)0.89Correct answer is option 'B'. Can you explain this answer?.
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