1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nesterboy [21]
3 years ago
14

An electron in the n = 6 level of the hydrogen atom relaxes to a lower energy level, emitting light of λ = 93.8 nm .find the pri

ncipal level to which the electron relaxed.
Physics
2 answers:
Xelga [282]3 years ago
7 0
We can find the lower level by using Rydberg's formula: 1/w = R(1/L² - 1/U²) where:

w - wavelength (9.38nm),

L - lower energy level

U - upper energy level (6); and

R - Rydberg's constant (10,967,758 waves per meter for hydrogen).

So plugging in the information above: 

1/ (9.38 * 10**-8 m.) = 10,967,758(1/L² - 1-36)

But we need to solve for L. 

The left side (1/9.38 * 10**-8) becomes 10,660,980

So translating:

10660980 = 10967758(1/L² - 0.02777777)

Then divide both sides by 10967758
we get: 0.9720291 = 1/L² - 0.02777777.

then add 0.02777777 to both sides 

we get: 0.9998 = 1/L² 

0.9998 is very close to 1, so we can approximate 1/L² = 1 so L = 1. 


Therefore the lower level is 1 which is the ground state.
Kipish [7]3 years ago
6 0

The principal energy level to which the electron relaxed is \boxed{n=1} .

Further Explanation:

When the transition of the electron from one energy level to another energy level takes place, there is an emission of the particular wavelength according to the energy of the level. The relation between the energy of emission and the wavelength is given as:

E=\frac{{hc}}{\lambda }

Substitute the value of the Planck’s constant, speed of light and the wavelength of the emitted light in the above expression.

\begin{aligned}E&=\frac{{\left({6.63\times{{10}^{-34}}}\right)\times\left({3\times{{10}^8}}\right)}}{{93.8\times{{10}^{-9}}}}\\&=2.12\times{10^{-18}}\,{\text{J}}\\\end{aligned}

This amount of energy is the change in the energy level as the electronic transition takes place.

The energy of the different energy levels in a hydrogen atom is expressed as:

\Delta E=13.6\,{\text{eV}}\left({\frac{1}{{n_f^2}}-\frac{1}{{n_i^2}}}\right)

Here, \Delta E  is the change in the energy, {n_f}  is the final energy level and {n_i}  is the initial energy level.

Substitute the values in the above expression.

\begin{aligned}2.12\times{10^{-18}}&=13.6\times\left({1.6\times{{10}^{-19}}}\right)\left({\frac{1}{{n_f^2}}-\frac{1}{{{6^2}}}}\right)\\\frac{{2.12\times{{10}^{-18}}}}{{2.176\times{{10}^{-18}}}}&=\frac{1}{{n_f^2}}-\frac{1}{{36}}\\\frac{1}{{n_f^2}}&=0.97+\frac{1}{{36}}\\{n_f}&\approx 1\\\end{aligned}

Thus, the principal energy level to which the electron relaxed is \boxed{n=1} .

Learn More:

1. Microwave ovens emit microwave energy with a wavelength of 12.5 cm. What is the energy of exactly one photon of this microwave radiation <u>brainly.com/question/2385939 </u>

2. What is the kinetic energy of the emitted electrons when cesium is exposed to uv rays of frequency 1.9×1015hz <u>brainly.com/question/9059731 </u>

3. When the atom's electrons step down to lower energy levels in a thin cloud of hot gas, what is produced <u>brainly.com/question/6054540 </u>

Answer Details:

Grade: High School

Subject: Physics

Chapter: Hydrogen spectrum

Keywords:

Electron, level n=6, hydrogen atom, transition of electron, lower energy level, emitting light, wavelength, 93.8 nm, principal level, electron relaxed.

You might be interested in
In comparison with other ocean basins, major sedimentary features such as continental rises and abyssal plains are relatively ra
Maksim231197 [3]

Answer:

Why are continental rises and abyssal plains relatively rare in the Pacific? This is because the extensive system of trenches along the active margins of the Pacific, trap much of the sediments flowing off the continents, preventing them from building the broad, flat abyssal plains typical of the Atlantic ocean basins.

3 0
3 years ago
Maureen takes notes in class. Wave Interactions
Monica [59]
A. <span>I .................
</span>
7 0
2 years ago
Read 2 more answers
What happens to an electromagnetic wave as it passes from space to matter?
alina1380 [7]

Answer:

When an electromagnetic wave passes from space to matter, some part of the energy is absorbed by the matter and it increases its energy. The wave may reflect and some part may pass through the matter depending on the amount of energy they have. The amplitude of the wave decreases if some parts of it are reflected.

4 0
2 years ago
Read 2 more answers
Describe three pieces of evidence that support the Big Bang theory
lisov135 [29]

Explanation :

According to astronomers, the whole universe is started with a giant explosion called as Big Bang. Big Bang theory shows that the universe is  extended from high density state.

There are some evidence for big bang as :

(1) There are some red shifts of different galaxies which means that the universe is expanding.  

(2) Due to the expanding of universe, some of the new elements are created like hydrogen, deuterium etc.

(3) Microwaves are detected by orbiting detectors.

All this parameters shows that big bang theory was correct.

6 0
3 years ago
Read 2 more answers
3. A motorbike travels 45 miles in 15 minutes, what is its speed?
antiseptic1488 [7]
Hes going 180 mph
oof...
3 0
3 years ago
Other questions:
  • Need help with this science!!
    5·1 answer
  • A single point charge q is located at the center of both an imaginary cube and an imaginary sphere. How does the electric flux t
    7·1 answer
  • How is speed determined?
    13·1 answer
  • HELP QUICK WILL GIVE BRAINLEST!!!!
    8·2 answers
  • Match the term to the correct description.
    14·2 answers
  • Find the magnitude of the resultant of forces 6N and 8N acting at 240° to each other
    15·1 answer
  • A car accelerates from rest at 3.00 m/second squared What is the velocity after 5 secs ? What is the displacement after 5 second
    6·1 answer
  • A man is picked up by a tornado and dropped a quarter mile away from his home. Even though authorities estimate that his body wa
    15·1 answer
  • How does the density of water change when: (a) it is heated from 0o
    5·1 answer
  • A pendulum has a mass of 0.060 kg swinging at a small angle from a light string, with a period of 1.4 s. What is the length of t
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!