We appreciate your visit to An electron is confined in the ground state in a 1D box 0 x a of width 1 Å Its energy is 37 6 eV. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
The energy of the electron in the first excited state is 0.376 eV.
Explanation:
To find the energy of the electron in the first excited state, we can use the formula for the energy levels of a particle confined in a 1D box:
E_n = (n^2 * h^2) / (8 * m * L^2)
Given that the electron is in the ground state with an energy of 37.6eV, we can substitute n = 1 and solve for the energy of the first excited state.
Plugging in the values:
E_1 = (1^2 * h^2) / (8 * m * L^2)
Since the width of the box is given as 1A, we can substitute L = 1A = 1 * 10^-10 m.
Now, we need to convert the energy from electron volts (eV) to joules (J) using the conversion factor: 1 eV = 1.6 * 10^-19 J.
Substituting the values and converting the units:
E_1 = (1^2 * (6.626 * 10^-34 J s)^2) / (8 * (9.109 * 10^-31 kg) * (1 * 10^-10 m)^2)
E_1 = (1 * (6.626 * 10^-34 J s)^2) / (8 * (9.109 * 10^-31 kg) * (1 * 10^-20 m^2))
E_1 = (6.626^2 * 10^-34 * 10^-34) / (8 * 9.109 * 10^-31 * 10^-20)
E_1 = (43.89 * 10^-68) / (72.872 * 10^-51)
E_1 = 0.602 * 10^-17 J
Converting back to electron volts:
E_1 = 0.602 * 10^-17 J * (1 eV / 1.6 * 10^-19 J)
E_1 = 0.376 eV
Therefore, the energy of the electron in the first excited state is 0.376 eV.
Learn more about energy of an electron in a 1d box here:
https://brainly.com/question/32199763
#SPJ14
Thanks for taking the time to read An electron is confined in the ground state in a 1D box 0 x a of width 1 Å Its energy is 37 6 eV. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
Final answer:
The energy of the electron in the first excited state is 0.376 eV.
Explanation:
To find the energy of the electron in the first excited state, we can use the formula for the energy levels of a particle confined in a 1D box:
E_n = (n^2 * h^2) / (8 * m * L^2)
Given that the electron is in the ground state with an energy of 37.6eV, we can substitute n = 1 and solve for the energy of the first excited state.
Plugging in the values:
E_1 = (1^2 * h^2) / (8 * m * L^2)
Since the width of the box is given as 1A, we can substitute L = 1A = 1 * 10^-10 m.
Now, we need to convert the energy from electron volts (eV) to joules (J) using the conversion factor: 1 eV = 1.6 * 10^-19 J.
Substituting the values and converting the units:
E_1 = (1^2 * (6.626 * 10^-34 J s)^2) / (8 * (9.109 * 10^-31 kg) * (1 * 10^-10 m)^2)
E_1 = (1 * (6.626 * 10^-34 J s)^2) / (8 * (9.109 * 10^-31 kg) * (1 * 10^-20 m^2))
E_1 = (6.626^2 * 10^-34 * 10^-34) / (8 * 9.109 * 10^-31 * 10^-20)
E_1 = (43.89 * 10^-68) / (72.872 * 10^-51)
E_1 = 0.602 * 10^-17 J
Converting back to electron volts:
E_1 = 0.602 * 10^-17 J * (1 eV / 1.6 * 10^-19 J)
E_1 = 0.376 eV
Therefore, the energy of the electron in the first excited state is 0.376 eV.
Learn more about energy of an electron in a 1d box here:
https://brainly.com/question/32199763
#SPJ14
