### Question 6: Photon Absorption in a Hydrogen Atom#### Problem Statement:A hydrogen atom absorbs a photon of visible light, and its electron enters the \( n = 4 \) energy level. Calculate the change in energy of the atom and the wavelength (in nm) of the photon.#### Choices:a) \( 20.4 \times 10^{-19} \) J and \( 97.44 \) nmb) \( 4.09 \times 10^{-19} \) J and \( 486 \) nmc) \( 5.09 \times 10^{-19} \) J and \( 4.86 \) nmd) \( 4.09 \times 10^{-19} \) J and \( 386 \) nm#### Explanation:To solve this problem, we need to use the relationship between the energy levels of the hydrogen atom and the energy of the absorbed photon. The energy change (\( \Delta E \)) when an electron transitions between energy levels in a hydrogen atom is given by:\[ \Delta E = E_4 - E_i \]Where \( E_4 \) is the energy of the \( n = 4 \) level and \( E_i \) is the energy level the electron transitioned from.Additionally, the energy (\( E \)) of the absorbed photon can be related to its wavelength (\( \lambda \)) by the equation:\[ E = \frac{hc}{\lambda} \]Where:- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \) Js)- \( c \) is the speed of light (\( 3.00 \times 10^8 \) m/s)- \( \lambda \) is the wavelength of the photon in metersBy matching the change in energy (\( \Delta E \)) with the given choices and using the respective equations, we can determine the correct option.

Given: Electron absorbs light and undergoes a transition from the ground state (ni is 1) to excited…

6. A hydrogen atom absorbs a photon of visible light, and its electron enters the n = 4 energy level. Calculate the change in energy of the atom and the wavelength (in nm) of the photon. a) 20.4 x 10-¹⁹ J and 97.44 nm b) 4.09 x 10-1⁹ J and 486 nm c) 5.09 x 10-¹⁹ J and 4.86 nm d) 4.09 x 10-19 J and 386 nm

6. A hydrogen atom absorbs a photon of visible light, and its electron enters the n = 4 energy level. Calculate the change in energy of the atom and the wavelength (in nm) of the photon. a) 20.4 x 10-¹⁹ J and 97.44 nm b) 4.09 x 10-1⁹ J and 486 nm c) 5.09 x 10-¹⁹ J and 4.86 nm d) 4.09 x 10-19 J and 386 nm

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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