Question

Please show your steps CLEARLY. I need to be able to read what you wrote and to follow your thinking. Thank you.

14. [1pt] Electrons accelerated by a potential difference of 13.14 V pass through a gas of hydrogen atoms at room temperature. Calculate the wavelength of light emitted with the longest possible wavelength. Submit All Answers Last Answer: 94.6nm Answer: Incorrect, tries 3/15. 15. [1pt] Calculate the wavelength of light emitted with the shortest possible wavelength. Answer: Submit All Answers

Answer 1

The electron possesses 13.14eV of energy as it is accelerated through 13.14V. As it passes through Hydrogen gas, it may collide with an electron and excite it to next higher energy level. When that excited electron falls back to its ground state, then we'll observe emitted wavelegths.

Energy difference between the ground state and first excited state of Hydrogen = 13.6eV - 3.4eV = 10.2eV

Minimum energy that is obtained upon returning of excited electron to ground state = 10.2eV

Therefore, maximum wavelngth, .

12400 = 121.56пт 10.2

Highest energy state that the electron can be escited to is n=5. Therefore when electron falls back to the ground state, it releases energy = 13.6eV - 0.54eV = 13.06eV

Therefore minimum wavelength, $\Lambda = \frac{12400}{13.06} = 94.95nm$