Bernard Boyer

2022-07-17

A hypothetical atom has two energy levels, with a transition wavelength between them of 580 nm. In a particular sample at 300 K, $4.0\cdot {10}^{20}$ such atoms are in the state of lower energy. (a) How many atoms are in the upper state, assuming conditions of thermal equilibrium? (b) Suppose, instead, that $3.0\cdot {10}^{20}$ of these atoms are “pumped” into the upper state by an external process, with $1.0\cdot {10}^{20}$ atoms remaining in the lower state. What is the maxi-mum energy that could be released by the atoms in a single laser pulse if each atom jumps once between those two states (either via absorption or via stimulated emission)?

Lillianna Mendoza

Beginner2022-07-18Added 16 answers

a) The upper level as level 1 and lower level as 2

Using

${N}_{1}={N}_{2}{e}^{-hc/\lambda KT}\phantom{\rule{0ex}{0ex}}=(4.0\times {10}^{20})exp-(\frac{1240eV\cdot nm}{580nm(8.62\times {10}^{-5}\text{}eV/K)300\text{}K})\phantom{\rule{0ex}{0ex}}=5.0\times {10}^{-15}\ll 1$

Thus, practically no electron occupies the upper level

Using

${N}_{1}={N}_{2}{e}^{-hc/\lambda KT}\phantom{\rule{0ex}{0ex}}=(4.0\times {10}^{20})exp-(\frac{1240eV\cdot nm}{580nm(8.62\times {10}^{-5}\text{}eV/K)300\text{}K})\phantom{\rule{0ex}{0ex}}=5.0\times {10}^{-15}\ll 1$

Thus, practically no electron occupies the upper level

Lorelei Patterson

Beginner2022-07-19Added 6 answers

(b) The maximum energy

The expression for the maximum energy is

${E}_{max}=({N}_{1}-{N}_{2}){E}_{photon}\phantom{\rule{0ex}{0ex}}=(3.0\times {10}^{20}-1.0\times {10}^{20})\frac{hc}{\lambda}\phantom{\rule{0ex}{0ex}}=(2.0\times {10}^{20})\frac{(6.63\times {10}^{-34}\text{}J\cdot s)(3\times {10}^{-3}\text{}m/s)}{580\times {10}^{-9}\text{}m}\phantom{\rule{0ex}{0ex}}=68.58\text{}J$

The expression for the maximum energy is

${E}_{max}=({N}_{1}-{N}_{2}){E}_{photon}\phantom{\rule{0ex}{0ex}}=(3.0\times {10}^{20}-1.0\times {10}^{20})\frac{hc}{\lambda}\phantom{\rule{0ex}{0ex}}=(2.0\times {10}^{20})\frac{(6.63\times {10}^{-34}\text{}J\cdot s)(3\times {10}^{-3}\text{}m/s)}{580\times {10}^{-9}\text{}m}\phantom{\rule{0ex}{0ex}}=68.58\text{}J$

The ground state energy of hydrogen atom is -13.6 eV. What are thekinetic and potential energies of the electron in this state?

The shortest and the longest wavelength in Balmer series of hydrogen spectrum are: Rydberg constant, ${R}_{H}=109678\text{}c{m}^{-1}$

Is atomic mass the sum of the number or mass of protons and neutrons.

If it is sum of number , then why is it called atomic MASS

And if it is sum of mass then how do we know the no of neutrons and proton sin the atom.Which is the smallest unit of matter? Atom or particle?

Who is the first person to propose the concept of an atom ?

Two different gases can have the same emission spectrum.

True or FalseHydrogen contains electron of n=1, Balmer Series requires electrons to jump from n=2 to n=3,4,5.... and again back to n=2. As n=2 is empty for Hydrogen atom, then how Balmer Series is formed for Hydrogen?

Fill the blank spaces for the list of properties of the Electromagnetic waves and EM spectrum: 1) In EM waves, $\overrightarrow{E},\overrightarrow{B}$ and the wave direction are mutually ____ 2) EM waves travel through space, carry and transfer ____ to the objects. 3) In electromagnetic spectrum,_____ have the lowest wavelength. 4) Of the seven different EM waves, _____ is used for security purposes.

Calculate the density of thermionic emission current in Cs at $500,1000,2000\text{}{k}^{\circ}$

To keep unwanted light from reflecting from the surface of eyeglasses or other lenses, a thin film of a material with an index of refraction n = 1.38 is coated onto the plastic lens (n = 1.55). What is the thinnest film that will minimize reflection for $\lambda =550\text{}nm$, the middle of the visible-light spectrum?

${}^{241}Am$ decays by alpha particle emission. The daughter isotope in this case is (the atomic numbers of Np, Pu, Am, Cm, and Bk are 91, 92, 93, 94, and 95 respectively)

${}^{235}Bk$

${}^{245}Bk$

${}^{239}Np$

not given

${}^{237}Np$A wavelength of $4.653\mu \text{}m$ is observed in a hydrogen spectrum for a transition that ends in the ${n}_{f}=5$ level. What was ${n}_{i}$ for the initial level of the electron?

What are the limiting frequencies and wavelengths for electron emission from sodium and from aluminum?

Explain why characteristic x rays are the most energetic in the EM emission spectrum of a given element.

Show that the entire Paschen series is in the infrared part of the spectrum. To do this, you only need to calculate the shortest wavelength in the series.