What is the longest wavelength light capable of ionizing a hydrogen atom in the n = 4 state?
i know that Solve h c/L = (Rydberg)/6^2 for L
something along those lines... but what am i solving for and what is c and h?
c is the speed of light. L is wavelength. YOu really ought to get familiar with equations you are using. Anyone can plug formulas.
so i would do speed of light/(rydberg)/6^2=h?
To find the longest wavelength light capable of ionizing a hydrogen atom in the n=4 state, you are solving for the wavelength (L). In this case, "c" represents the speed of light in a vacuum, and "h" represents Planck's constant.
First, let's break down the equation you have mentioned: h c/L = (Rydberg)/6^2
- "h" represents Planck's constant, which is a fundamental constant in quantum mechanics with the value of 6.62607015 × 10^-34 J·s.
- "c" represents the speed of light in a vacuum, which is approximately 3.00 × 10^8 m/s.
- "L" represents the wavelength of light you are solving for.
- "(Rydberg)" refers to the Rydberg constant, which is a physical constant used in atomic physics and is given by 1.0973731568508 × 10^7 m^-1.
Now, to solve for L, you can rearrange the equation:
L = (h c) / ((Rydberg)/6^2)
Let's substitute the values into the equation:
L = (6.62607015 × 10^-34 J·s * 3.00 × 10^8 m/s) / ((1.0973731568508 × 10^7 m^-1)/6^2)
Simplifying the equation further:
L = (1.98782119 × 10^-25 J·m) / (8.680363 × 10^5 m^-1)
Finally, dividing the two terms:
L ≈ 2.287 × 10^20 m
Therefore, the longest wavelength of light capable of ionizing a hydrogen atom in the n = 4 state is approximately 2.287 × 10^20 meters.