Question

What is the maximum wavelength to excite a hydrogen atom?

• A. \( \lambda = \frac{1}{13.6 \, \text{eV}} \)
• B. \( \lambda = \frac{c}{R} \)
• C. \( \lambda = \frac{h}{E} \)
• D. \( \lambda = \frac{c}{E} \)

Hint:

The maximum wavelength corresponds to the minimum energy required for excitation. For hydrogen, this can be calculated using \( \lambda = \frac{h}{E} \).

Answer 1

The Correct Option is C

In the hydrogen atom, the energy of the electron is quantized and can be given by: \[ E = \frac{1
3.6 \, \text{eV}}{n^2} \] where \( n \) is the principal quantum number, and \( 1
3.6 \, \text{eV} \) is the ground state energy of hydrogen. To excite the electron, we need to provide energy equal to or greater than the energy difference between the levels. The maximum wavelength corresponds to the minimum energy needed for excitation. The energy and wavelength of a photon are related by: \[ E = \frac{h c}{\lambda} \] where \( h \) is Planck's constant and \( c \) is the speed of light. Solving for wavelength, we get: \[ \lambda = \frac{h}{E} \] Thus, the maximum wavelength corresponds to the energy required to excite the hydrogen atom, and the formula is \( \lambda = \frac{h}{E} \).