A H atom absorbs a photon with a wavelength of 9.50 × 10^1 nm. If the energy of the final state of the H atom was -8.72 × 10^(-20) J, calculate the energy of the initial state. Express answer in scientific notation

Question

A H atom absorbs a photon with a wavelength of 9.50 × 10^1 nm. If the energy of the final state of the H atom was -8.72 × 10^(-20) J, calculate the energy of the initial state. Express answer in scientific notation

Answer 1

delta E = hc/wavelength; solve for delta E.

delta E = E1-E2
dE = Efinal - Einitial
Solve for Einitial.

Answer 2

To calculate the energy of the initial state of the H atom, we can use the energy-wavelength relationship given by the equation:

E = hc / λ

Where E is the energy, h is Planck's constant (6.62607015 x 10^-34 J·s), c is the speed of light (2.998 x 10^8 m/s), and λ is the wavelength.

First, let's convert the given wavelength of 9.50 × 10^1 nm to meters:

λ = 9.50 × 10^1 nm = (9.50 × 10^1) x (1 × 10^-9) m = 9.50 × 10^-8 m

Now we can plug the values into the equation to calculate the energy of the initial state:

E = (6.62607015 × 10^-34 J·s) x (2.998 × 10^8 m/s) / (9.50 × 10^-8 m)

E = (6.62607015 × 2.998) / 9.50 × (10^-34 x 10^8) / (10^-8)

E = 19.8408187 x 10^(-26 - 8 + 8)

E = 19.8408187 x 10^(-26)

Now, express the answer in scientific notation:

E = 1.98408187 × 10^-25 J

Therefore, the energy of the initial state of the H atom is 1.98408187 × 10^-25 J.

Answer 3

To calculate the energy of the initial state of the hydrogen atom, you need to find the difference in energy between the final and initial states.

First, convert the given wavelength from nm (nanometers) to meters.

Given: wavelength = 9.50 × 10^1 nm

1 nm = 1 × 10^(-9) meters

So, 9.50 × 10^1 nm = 9.50 × 10^(-9) meters

Now, you can use the equation E = hc/λ, where E is energy, h is Planck's constant (6.626 x 10^(-34) J·s), c is the speed of light (3.00 × 10^8 m/s), and λ is the wavelength.

E = (6.626 × 10^(-34) J·s * 3.00 × 10^8 m/s) / (9.50 × 10^(-9) m)

Simplifying this equation gives:

E = 1.98 × 10^(-25) J

This is the energy of the final state of the hydrogen atom (-8.72 × 10^(-20) J).

Now, to find the energy of the initial state, you need to subtract the energy difference between the two states:

Initial state energy = Final state energy + Energy difference

Initial state energy = -8.72 × 10^(-20) J + 1.98 × 10^(-25) J

Simplifying this equation gives:

Initial state energy = -8.72 × 10^(-20) J + 0 J = -8.72 × 10^(-20) J

Therefore, the energy of the initial state of the hydrogen atom is -8.72 × 10^(-20) J, as given in the problem statement.