# Atomic Structure

# Electromagnetic Waves

^{8}m/s. The electromagnetic spectrum ranges from radio waves to gamma rays.

# The Wave Nature

**wave length**(Î»).

**Frequency**(f) is the number of wavelengths passing through a point in unit time. Wavelength and frequency are related by the relation given below. Frequency is usually expressed in 1/second (s

^{â€“1}), which is otherwise known as

*hertz*(Hz).

Velocity = frequency x wavelength

c = f Î»

# The Particle Nature and Quantum Theory

Energy = *h* f,

where *h* is the Planck's constant, and f is the frequency.

Planck's constant = 6.63 x 10^{â€“34} J.s

**Heisenberg's Uncertainty Principle**, we cannot determine both the momentum and the position of subatomic particles simultaneously. This is because we are using other particles (electromagnetic particles-like photons) of comparable energy to detect these subatomic particles, and by the time these other particles find the subatomic particles (say electrons), they are also disturbing the pathway of these electrons. In essence, the study of something extremely small and fast (about the magnitude of electrons) cannot be done without interference of its natural course or position.

# Photoelectric Effect

*threshold frequency*. The required threshold frequency is a characteristic specific to each metal. Experimentally, it has been found that the photoelectrons emitted with maximum energy do not have the full energy equivalent supplied by the incident photon. This is because energy is required to break loose the electrons from the surface of the metal. The energy required for this is called "work function," which is characteristic of each metal. The photoelectrons can be accelerated to a positively charged plate, creating a flow of charges along a wire-photocurrent. The current can be measured by an ammeter connected to the wire.

The maximum kinetic energy (*K*_{max}) of a photoelectron is given by the following equation:

*K*_{max} = 1/2 *mv*_{max}^{2} = *hf* â€“ *Ï•*

In this equation, *m* is the mass of an electron, *v*_{max}is the maximum velocity of the electrons, *h* is the Planck's constant, *f* is the frequency of the incident light, *Ï•* (pronounced *phi*) is the "work function" of the metal. The entity *hf* represents the energy of the incident photon.

# Key Observations on Photoelectric Effect

- The photoelectric effect exemplifies the particle nature of light.
- Based on conservation of energy, no photoelectron can have energy more than that of an incident photon.
- The energy of the photoelectrons is always less than that of the incident photons, because some energy (work function) is required to break the electrons loose.
- The maximum energy of the photoelectrons is independent of the intensity of the incident light.
- Electrons are not ejected no matter how high the intensity of the incident light is, unless the incident light has the energy corresponding to the threshold frequency characteristic of a particular metal.

# Atomic Emission Spectra

*continuous spectrum*of wavelengths. Another type of spectrum results when heated gas emits light. This results in a

*line spectrum*. Line spectrum contains only certain specific wavelengths of light. The wavelengths in the visible spectrum of hydrogen is given by the following formula:

*R*(Rydberg constant) = 2.18 x 10

^{â€“18}J,

*h*(Planck's constant) = 6.63 x 10

^{â€“34}J.s,

*c*(speed of light) = 3.0 x 10

^{8}m/s, and

*n*is some whole number that is greater than 2 which corresponds to the orbit-number from which the electron is making the transition. For example, if the transition of an electron is from orbit number 4 to 2, the

*n*value is 4.

# Bohr's Model of Hydrogen Atom

- In each hydrogen atom, the electron revolves around the nucleus in one of the several stable orbits.
- Each orbit has a definite radius and thus has a definite energy associated with it.
- An electron in an orbit closest to the nucleus has the lowest energy, and if the electron is in the lowest orbit the atom is said to be in its
*ground state*. - The electron in an atom may absorb discrete amounts of energy and move to another orbit with higher energy, and this state is called the
*excited state*. - An electron in an excited atom can go back to a lower energy level and this process will result in the release of excess energy as light.
- The amount of energy released or absorbed is equal to the difference between the energies of the initial and final orbits.

*E*

_{initial}) jumps to a lower energy level (

*E*

_{final}). Based on the law of conservation of energy, the sum of energies of the emitted photon (

*hf*) and the electron's final energy (

*E*

_{final}) should be equal to the electron's initial energy (

*E*

_{initial}). This can be represented mathematically as follows:

*hf* + *E*_{final} = *E*_{initial}

*n*

_{final}and

*n*

_{inital}are the principal quantum numbers of final and initial energy levels, and

*R*is the Rydberg constant (2.18 x 10

^{â€“18}

_{final}values 1, 2, and 3, respectively.

*A photon is emitted when an electron in an atom jumps from a higher to a lower energy level. The energy of the emitted photon is equal to the difference in energy between the two energy levels.*