Calculate the wavelength of the light emitted when an electron in a hydrogen atom makes each transition and indicate the region of the electromagnetic spectrum (infrared, visible, ultraviolet, etc.) where the light is found. a. n = 2 → n = 1 b. n = 3 → n = 1 c. n = 4 → n = 2 d. n = 5 → n = 2

검증된 단계별 안내

Identify the formula to calculate the wavelength of light emitted during an electron transition in a hydrogen atom: \( \frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \), where \( R_H \) is the Rydberg constant (1.097 \(\times\) 10^7 \(\text{ m}\)^{-1}), \( n_1 \) is the lower energy level, and \( n_2 \) is the higher energy level.

For each transition, substitute the given values of \( n_1 \) and \( n_2 \) into the formula to find \( \frac{1}{\lambda} \).

Calculate \( \lambda \) by taking the reciprocal of \( \frac{1}{\lambda} \).

Convert the wavelength from meters to nanometers by multiplying by \( 10^9 \) (since 1 m = 10^9 nm).

Determine the region of the electromagnetic spectrum by comparing the calculated wavelength to known ranges: infrared (> 700 nm), visible (400-700 nm), ultraviolet (< 400 nm).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

15m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Energy Levels in Hydrogen Atom

In a hydrogen atom, electrons occupy specific energy levels, denoted by quantum numbers (n). When an electron transitions between these levels, it either absorbs or emits energy in the form of light. The energy difference between the levels determines the wavelength of the emitted light, which can be calculated using the Rydberg formula.

Wavelength and Frequency Relationship

The wavelength of light is inversely related to its frequency, as described by the equation c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency. This relationship is crucial for determining the wavelength of light emitted during electron transitions in the hydrogen atom, as the energy of the emitted photon can be calculated from the frequency.

Regions of the Electromagnetic Spectrum

The electromagnetic spectrum is divided into various regions based on wavelength and frequency, including infrared, visible, and ultraviolet light. The wavelength calculated from electron transitions in a hydrogen atom will fall into one of these regions, which helps in identifying the type of light emitted. For example, transitions from higher energy levels often result in ultraviolet light, while lower energy transitions may emit visible or infrared light.