The hydrogen atom can absorb light of wavelength 1094 nm. (b) Determine the final value of n associated with this absorption.

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Hey everyone in this example, we need to solve for the final energy state. End of an electron in a hydrogen atom that absorbed a wavelength of 487 nanometers of light if its initial energy state is at the second energy level. So what we want to recall is our formula where the energy of a photon of light is equal to Planck's constant, multiplied by our speed of light, divided by our wavelength which is then set equal to negative one times our rights burg constant, which is multiplied by the difference between one over our final energy level squared minus one over our initial energy level squared. So what we're going to have when we plug in the info from the problem is that We're going to recall our plank's constant. H is 6.626 times 10 to the negative 34th power. It's in units of jewels time seconds. And we're going to recall that our value for the speed of light C. Is going to be three times 10 to the eighth power meters per second. We're then going to divide this by our wavelength given in the prompt as 487 nanometers. But because we want our units of meters to cancel out in the new meter, we're going to convert from nanometers two m by recalling that we have 4 10 to the ninth power nanometers one m because our prefix nano means 10 to the ninth power. So now we're able to cancel out nanometers leaving us with meters so that we're able to also cancel out meters as well as seconds leaving us with units of jewels for our final answer. And this is going to be Equal to the right hand side of our equation where we take negative one times our rights burg constant, which we would recall is equal to 2.18 times 10 to the negative 18th power and units of jewels. And just to make more room, we're going to size this down. So this Rydberg constant is then multiplied by one over our final energy level which is what we're solving for squared and then subtracted from one over our initial energy level. Given in the prompt as two squared. So what we're going to do now is utilize the solver function either online or in our calculators to solve for our final energy level. And so what we should get is that our final energy level is equal to a value of 3.99, which we can round to one sig Fig which would be four. And so this would be our final answer for the final energy level. Where are electron in a hydrogen atom ends up at after. It absorbs a wavelength of 487 nanometers. So four is our final answer. If you have any questions please leave them down below and I will see everyone in the next practice video

The hydrogen atom can absorb light of wavelength 1094 nm. (b) Determine the final value of n associated with this absorption.

Verified Solution

Key Concepts

Energy of Photons

Quantum Energy Levels

Balmer and Rydberg Formulas