To understand the relationship between the assertion and the reason provided, we need to delve into the concepts of photon energy, electron transitions, and the behavior of hydrogen atoms in their ground state. Let's break this down step by step.
Photon Energy and Electron Transitions
Photons are particles of light that carry energy, which can be calculated using the equation:
E = hν
where E is the energy of the photon, h is Planck's constant, and ν is the frequency of the light. In this case, we have photons with an energy of 10.0 eV.
Ground State of Hydrogen
Hydrogen, the simplest atom, has its electron in the ground state at an energy level of -13.6 eV. When we talk about transitions to excited states, we refer to the energy levels that the electron can occupy when it absorbs energy. The first excited state of hydrogen is at -3.4 eV, and the energy difference between the ground state and the first excited state is:
ΔE = E(excited) - E(ground) = -3.4 eV - (-13.6 eV) = 10.2 eV
Energy Absorption and Transmission
For an electron to transition from the ground state to an excited state, it must absorb a photon with energy equal to or greater than the energy difference between these states. In this case, the minimum energy required for the transition to the first excited state is 10.2 eV. Since the energy of the incident photons is only 10.0 eV, which is less than 10.2 eV, the electrons in the hydrogen atoms cannot absorb this energy.
Implications for Photon Transmission
Since the photons do not have enough energy to excite the electrons, they will not be absorbed by the hydrogen gas. Instead, they will pass through the gas without any interaction. This leads us to the assertion that the beam of photons is completely transmitted through the gas without absorption.
Connecting the Assertion and Reason
Both the assertion and the reason are true. The assertion states that the beam of photons is transmitted through the hydrogen gas without absorption, which is correct because the energy of the photons is insufficient to excite the electrons. The reason provides the necessary context by explaining that the minimum energy required for an electron to transition to an excited state is 10.2 eV, which is greater than the energy of the incident photons (10.0 eV). Therefore, the reason effectively explains why the assertion holds true.
Summary
- The energy of the incident photons (10.0 eV) is less than the energy required for an electron transition (10.2 eV).
- As a result, the photons are not absorbed by the hydrogen atoms.
- This leads to the conclusion that the beam of photons is transmitted completely through the gas.
In essence, the reason clarifies the mechanism behind the assertion, making it a valid explanation for why the photons pass through the hydrogen gas without being absorbed.
