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The energy of a linear harmonic oscillator in third excited state is 4.1eV. The frequency of vibration is (h= 6.62 * 10 ^ - 34 * J -sec )
(a) 3.3 × 1013Hz
(b 2.8 * 10 ^ 13 * Hz
(d) 4.2 ×10¹³Hz
(c) 3.9 x 10^13 Hz?
(a) 3.3 × 1013Hz
(b 2.8 * 10 ^ 13 * Hz
(d) 4.2 ×10¹³Hz
(c) 3.9 x 10^13 Hz?
Most Upvoted Answer
The energy of a linear harmonic oscillator in third excited state is 4...
Understanding the Problem
To find the frequency of vibration of a linear harmonic oscillator in its third excited state, we start with the known energy levels of the oscillator. The energy of a quantum harmonic oscillator is given by:
E_n = (n + 1/2) * h * f
where E_n is the energy of the nth state, h is Planck's constant, f is the frequency, and n is the quantum number (n = 0 for the ground state, n = 1 for the first excited state, etc.).
Given Information
- Energy of the third excited state (n = 3): E_3 = 4.1 eV
- Planck’s constant (h): 6.62 * 10^(-34) J·s
- We need to convert eV to joules: 1 eV = 1.6 * 10^(-19) J
Energy Conversion
- E_3 in joules = 4.1 eV * 1.6 * 10^(-19) J/eV = 6.56 * 10^(-19) J
Calculating Frequency
Using the formula for energy:
E_3 = (3 + 1/2) * h * f
This simplifies to:
6.56 * 10^(-19) J = (7/2) * (6.62 * 10^(-34) J·s) * f
Rearranging for f gives:
f = (6.56 * 10^(-19) J) / ((7/2) * (6.62 * 10^(-34) J·s))
Calculating f:
- f = (6.56 * 10^(-19)) / (2.31 * 10^(-34))
- f ≈ 2.84 * 10^(13) Hz
Final Answer
The closest option to our calculated frequency is:
- (b) 2.8 * 10^(13) Hz
To find the frequency of vibration of a linear harmonic oscillator in its third excited state, we start with the known energy levels of the oscillator. The energy of a quantum harmonic oscillator is given by:
E_n = (n + 1/2) * h * f
where E_n is the energy of the nth state, h is Planck's constant, f is the frequency, and n is the quantum number (n = 0 for the ground state, n = 1 for the first excited state, etc.).
Given Information
- Energy of the third excited state (n = 3): E_3 = 4.1 eV
- Planck’s constant (h): 6.62 * 10^(-34) J·s
- We need to convert eV to joules: 1 eV = 1.6 * 10^(-19) J
Energy Conversion
- E_3 in joules = 4.1 eV * 1.6 * 10^(-19) J/eV = 6.56 * 10^(-19) J
Calculating Frequency
Using the formula for energy:
E_3 = (3 + 1/2) * h * f
This simplifies to:
6.56 * 10^(-19) J = (7/2) * (6.62 * 10^(-34) J·s) * f
Rearranging for f gives:
f = (6.56 * 10^(-19) J) / ((7/2) * (6.62 * 10^(-34) J·s))
Calculating f:
- f = (6.56 * 10^(-19)) / (2.31 * 10^(-34))
- f ≈ 2.84 * 10^(13) Hz
Final Answer
The closest option to our calculated frequency is:
- (b) 2.8 * 10^(13) Hz
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The energy of a linear harmonic oscillator in third excited state is 4.1eV. The frequency of vibration is (h= 6.62 * 10 ^ - 34 * J -sec )(a) 3.3 × 1013Hz(b 2.8 * 10 ^ 13 * Hz(d) 4.2 ×10¹³Hz(c) 3.9 x 10^13 Hz?
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The energy of a linear harmonic oscillator in third excited state is 4.1eV. The frequency of vibration is (h= 6.62 * 10 ^ - 34 * J -sec )(a) 3.3 × 1013Hz(b 2.8 * 10 ^ 13 * Hz(d) 4.2 ×10¹³Hz(c) 3.9 x 10^13 Hz? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about The energy of a linear harmonic oscillator in third excited state is 4.1eV. The frequency of vibration is (h= 6.62 * 10 ^ - 34 * J -sec )(a) 3.3 × 1013Hz(b 2.8 * 10 ^ 13 * Hz(d) 4.2 ×10¹³Hz(c) 3.9 x 10^13 Hz? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The energy of a linear harmonic oscillator in third excited state is 4.1eV. The frequency of vibration is (h= 6.62 * 10 ^ - 34 * J -sec )(a) 3.3 × 1013Hz(b 2.8 * 10 ^ 13 * Hz(d) 4.2 ×10¹³Hz(c) 3.9 x 10^13 Hz?.
The energy of a linear harmonic oscillator in third excited state is 4.1eV. The frequency of vibration is (h= 6.62 * 10 ^ - 34 * J -sec )(a) 3.3 × 1013Hz(b 2.8 * 10 ^ 13 * Hz(d) 4.2 ×10¹³Hz(c) 3.9 x 10^13 Hz? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about The energy of a linear harmonic oscillator in third excited state is 4.1eV. The frequency of vibration is (h= 6.62 * 10 ^ - 34 * J -sec )(a) 3.3 × 1013Hz(b 2.8 * 10 ^ 13 * Hz(d) 4.2 ×10¹³Hz(c) 3.9 x 10^13 Hz? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The energy of a linear harmonic oscillator in third excited state is 4.1eV. The frequency of vibration is (h= 6.62 * 10 ^ - 34 * J -sec )(a) 3.3 × 1013Hz(b 2.8 * 10 ^ 13 * Hz(d) 4.2 ×10¹³Hz(c) 3.9 x 10^13 Hz?.
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