Calculate Energy & Wavelength of Hydrogen Atom Absorption

In summary, The hydrogen atom can absorb light of wavelength 4055nm and the initial and final values of n associated with this absorption are 4 and 5. The energy absorbed is 4.905 * 10^-20 J and to solve for the unknowns, one can use the equation 1/nf^2 - 1/ni^2 = -.0225 and guess and check for the values of n.
  • #1
needhelpperson
112
0
The hydrogen atom can absorb light of wavelength 4055nm. Determine the inital and final values of n associated with this absorption.

Well i figured out the Energy it absorbed

(h*c)/(wavelength)

= ((6.63*10-34)*(3*10^8))/(4055/10^9)

=4.905 * 10^-20 J

so 4905*10^-20 = -2.18*10-18*(1/nf^2 - 1/ni^2)

1/nf^2 - 1/ni^2 = -.0225

How do i solve these two unknowns, other than guess and check?
 
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  • #2
I think its pretty much guess and check from there. I get 5 and 4.
 
  • #3
Healey01 said:
I think its pretty much guess and check from there. I get 5 and 4.

ya i got the same answers... but i just wanted to see if anyone has a different method to solve this problem .
 

FAQ: Calculate Energy & Wavelength of Hydrogen Atom Absorption

What is the formula for calculating the energy of a hydrogen atom absorption?

The formula for calculating the energy of a hydrogen atom absorption is E = -13.6/n2 eV, where n is the principal quantum number.

How do I calculate the wavelength of a hydrogen atom absorption?

The formula for calculating the wavelength of a hydrogen atom absorption is λ = c/f, where c is the speed of light (2.998 x 108 m/s) and f is the frequency of the absorbed photon. The frequency can be calculated using the Rydberg formula: 1/λ = R(1/n12 - 1/n22), where R is the Rydberg constant (1.097 x 107 m-1).

What is the Rydberg constant and how is it related to hydrogen atom absorption?

The Rydberg constant (R) is a fundamental physical constant that appears in the Rydberg formula for calculating the frequency of a photon absorbed or emitted by a hydrogen atom. It is related to hydrogen atom absorption because it helps determine the energy levels of the atom and thus the wavelengths of absorbed or emitted photons.

Can the energy and wavelength of a hydrogen atom absorption be measured experimentally?

Yes, the energy and wavelength of a hydrogen atom absorption can be measured experimentally using spectroscopy techniques. By analyzing the spectrum of light emitted or absorbed by a hydrogen atom, the energy and wavelength of the absorption can be determined.

How does the energy and wavelength of hydrogen atom absorption change with different energy levels?

The energy and wavelength of hydrogen atom absorption change with different energy levels due to the relationship between the energy and principal quantum number (n). As the value of n increases, the energy and wavelength of absorption also increase, meaning that photons with higher energy and shorter wavelengths are absorbed by the atom. This is known as the Balmer series, which is a series of specific wavelengths of light that are absorbed by a hydrogen atom at different energy levels.

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