Hydrogen Atom's Energy Levels-True/False

In summary, the statements about the hydrogen atom's energy levels include: the ground state energy is -13.6 eV, the wavelength of a photon emitted from the n=3 to n=2 transition is longer than that emitted for the n=4 to n=3 transition, 13.6 eV is enough energy to ionize hydrogen, and the hydrogen atom in its ground state cannot absorb a photon of any energy greater than 13.6 eV. However, the statement that the hydrogen atom in its ground state can absorb a photon of any energy less than 13.6 eV is FALSE.
  • #1
sona1177
173
1

Homework Statement


Which of the following statements are true about the hydrogen atom's energy levels?

the ground state (n = 1) energy is -13.6 eV TRUE

the wavelength of a photon emitted from the n=3 to n=2 transition is longer than that emitted for the n=4 to n=3 transition FALSE

13.6 eV is enough energy to ionize hydrogen, which means exciting an electron from n = 1 up to zero energy TRUE

the hydrogen atom in its ground state can absorb a photon of any energy less than 13.6 eV FALSE

the hydrogen atom in its ground state cannot absorb a photon of any energy greater than 13.6 eV
TRUE

WHAT AM I DOING WRONG??

Homework Equations





The Attempt at a Solution

 
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  • #2
"What am I doing wrong" is a fairly vague question...
 
  • #3
Pengwuino said:
"What am I doing wrong" is a fairly vague question...

I realize that, but since its true and false, I don't know how else to ask.
 
  • #4
sona1177 said:
I realize that, but since its true and false, I don't know how else to ask.

So you're asking if what you have is right or wrong?
 
  • #5
Pengwuino said:
So you're asking if what you have is right or wrong?

Well I know at least one of the answers is wrong because I am getting marked incorrect.

Im thinking the third and last one are both false. Because if n>1 then that would be an excited state. is this right? thanks!
 
  • #6
would all of them be false except the first one? because if its in the excited state then n>1 and then E >13.6eV? I know the first and second ones are correct for sure :)
 
  • #7
If you're talking about n>1 for the 2nd problem, it's not really what's being asked. Both transitions are acceptable and they will emit a photon. However they'll be different energy photons and it's basically asking which will have a larger wavelength (and you picked correctly). The last question I believe is wrong. I'm pretty sure you can just have a scattering action from the extra energy but I'm not certain.

Actually don't take my word on this stuff, it's been a while since I've done NR QM...
 
  • #8
Sorry I don't think I am thinking straight here.

If En=E1/n^2 where E1=-13.6 eV and n=1,2,3, then wouldn't E always be less than E1, then the fourth statement is true and the last is also true. so I would have:

the ground state (n = 1) energy is -13.6 eV TRUE

the wavelength of a photon emitted from the n=3 to n=2 transition is longer than that emitted for the n=4 to n=3 transition FALSE

13.6 eV is enough energy to ionize hydrogen, which means exciting an electron from n = 1 up to zero energy TRUE

the hydrogen atom in its ground state can absorb a photon of any energy less than 13.6 eV TRUE

the hydrogen atom in its ground state cannot absorb a photon of any energy greater than 13.6 eV
TRUE

IS this correct?
 
  • #9
Pengwuino said:
If you're talking about n>1 for the 2nd problem, it's not really what's being asked. Both transitions are acceptable and they will emit a photon. However they'll be different energy photons and it's basically asking which will have a larger wavelength (and you picked correctly). The last question I believe is wrong. I'm pretty sure you can just have a scattering action from the extra energy but I'm not certain.

Actually don't take my word on this stuff, it's been a while since I've done NR QM...

well i found out the last two are true. but its still marking me wrong when i have

True
false
true
true
true

Could the third one be wrong?
 
  • #10
Statement - the hydrogen atom in its ground state cannot absorb a photon of any energy greater than 13.6 eV.

It is FALSE.

because it can absorb a photon of greater energy, be ionized and the extra energy is converted to kinetic energy of the electron.
 
  • #11
supratim1 said:
Statement - the hydrogen atom in its ground state cannot absorb a photon of any energy greater than 13.6 eV.

It is FALSE.

because it can absorb a photon of greater energy, be ionized and the extra energy is converted to kinetic energy of the electron.

SO IS IT GOING TO BE:


Which of the following statements are true about the hydrogen atom's energy levels?

the ground state (n = 1) energy is -13.6 eV TRUE

the wavelength of a photon emitted from the n=3 to n=2 transition is longer than that emitted for the n=4 to n=3 transition FALSE

13.6 eV is enough energy to ionize hydrogen, which means exciting an electron from n = 1 up to zero energy TRUE

the hydrogen atom in its ground state can absorb a photon of any energy less than 13.6 eV TRUE

the hydrogen atom in its ground state cannot absorb a photon of any energy greater than 13.6 eV
FALSE
 
  • #12
Statement - the hydrogen atom in its ground state can absorb a photon of any energy less than 13.6 eV

is FALSE.

it can only absorb discrete energies less than 13.6ev, which correspond to energy difference between level 1 and some upper level.
 
  • #13
THANKS, SUPRATIM. LET ME TRY AGAIN (I AM SUBMITTING THIS FOR HOMEWORK AND IM ON MY LAST TRY SO IF I GET THIS WRONG, I WILL LOSE ALL THE POINTS, SO I WANT TO DOUBLE CHECK):

Which of the following statements are true about the hydrogen atom's energy levels?

the ground state (n = 1) energy is -13.6 eV TRUE

the wavelength of a photon emitted from the n=3 to n=2 transition is longer than that emitted for the n=4 to n=3 transition FALSE

13.6 eV is enough energy to ionize hydrogen, which means exciting an electron from n = 1 up to zero energy TRUE

the hydrogen atom in its ground state can absorb a photon of any energy less than 13.6 eV FALSE

the hydrogen atom in its ground state cannot absorb a photon of any energy greater than 13.6 eV
FALSE
 
  • #14
welcome Sona. yes you are right now. all the best for your homework, you will surely get full marks. :-)
 
  • #15
supratim1 said:
welcome Sona. yes you are right now. all the best for your homework, you will surely get full marks. :-)

Thanks, Supratim! I got this one right. Now onto the other Rutherford one . . .
 

1. Is the energy of the hydrogen atom's energy levels quantized?

Yes, the energy of the hydrogen atom's energy levels is quantized, meaning it can only have specific, discrete values. This is a fundamental concept in quantum mechanics.

2. Are the energy levels of the hydrogen atom evenly spaced?

No, the energy levels of the hydrogen atom are not evenly spaced. The spacing between energy levels decreases as the energy level increases, following a specific mathematical pattern.

3. Does the energy of the hydrogen atom's energy levels increase or decrease as the energy level increases?

The energy of the hydrogen atom's energy levels increases as the energy level increases. This can be seen in the energy level diagram, where the energy levels are arranged in increasing order from bottom to top.

4. Are the energy levels of the hydrogen atom affected by external factors?

Yes, the energy levels of the hydrogen atom can be affected by external factors such as electric and magnetic fields. This is known as the Stark and Zeeman effects, respectively.

5. Are the energy levels of the hydrogen atom the same for all atoms?

No, the energy levels of the hydrogen atom can vary slightly from atom to atom due to factors such as nuclear spin and isotopic abundance. However, the overall energy level structure remains the same.

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