Question

In hydrogen atom, energy of first excited state is -3.4 eV. Then, KE of same orbit of hydrogen atom :-

• A. +3.4 eV
• B. +6.8 eV
• C. -13.6 eV
• D. +13.6 eV

Hint:

Total energy \((E_n)\)= \(KE + PE\) 

Answer 1

The Correct Option is A

In hydrogen atom, energy of first excited state is -3.4 eV

Then, KE of same orbit of hydrogen atom can be determined by:

\(\because\) Total energy \((E_n)\)= \(KE + PE\) 
In first excited state\(=\frac{1}{2}mv^2+\Bigg[-\frac{Ze^2}{r}\Bigg]\)
\(\hspace15mm =+\frac{1}{2}\frac{Ze^2}{r}-\frac{Ze^2}{r}\) 

\(\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, - 3.4 eV =-\frac{1}{2}\frac{Ze^2}{r}\)
\(\therefore \, \, \, \, \, \, \, \, \, \, \, \, \, KE=\frac{1}{2}\frac{Ze^2}{r}\) 
= \(+\, 3.4 \,eV\)

So, Energy of first excited state is 3.4 eV 

The kinetic energy of a particle is the form of energy that it possesses due to the motion of the particle. It is also defined as the work done in accelerating a particle of a given mass from rest to its stated velocity.

• The motion of electrons, waves, atoms, substances, molecules, and objects are examples of kinetic energy.
• A system of bodies that is the combination of many individual bodies may have internal kinetic energy due to the motion of individual bodies.
• The SI unit of kinetic energy is joule (J).
• The kinetic energy of a body of mass m moving with velocity v is given by
  K.E = 1/2 mv²

Discover more from this chapter: Structure of Atom

Answer 2

The correct answer is Option A) +3.4 eV

Real Life Applications

• The application of the kinetic energy of the electron is as follows:
• To understand the emission spectrum of hydrogen. They are the lines that are generated when the electron moves from one state to another ( from excited to ground state). Lasers are used to generate light that is of a specific wavelength. To create a laser kinetic energy of an electron should be known.
• The atoms in the material are affected by the electric field generated. To study the properties of materials kinetic energy of electrons are studied.

Question can also be asked as

1. What is the kinetic energy of an electron in the first excited state of a hydrogen atom?
2. How is the kinetic energy of an electron related to the energy of the electron in an atom?

Answer 3

All forms of energy may be divided into two main categories: kinetic energy, or energy resulting from an object's motion, and potential energy, or energy held inside a body.

• The movement of electrons, waves, atoms, substances, molecules, and objects is a source of kinetic energy.
• Due to its location, an item stores potential energy.
• It can never be destroyed and may be kept in a variety of ways.
• Chemical, thermal, nuclear, electrical, mechanical, and a host of other forms of energy exist.
• Different units can be used to measure energy, and the SI unit for energy is the joule. 
• Other widely used units of energy exist in addition to the SI units, including calories, horsepower, kilowatts, megawatts, and barrels.

Energy Level Formula

The Bohr Model of the hydrogen atom should be taken into account when calculating the rotational energy level formula.

• In the standard model of the hydrogen atom, an assumption was made concerning the quantization of atoms.
• According to this theory, electrons orbit the nucleus in orbits or shells with a fixed radius.
• Only shells with a radius equal to the Energy Level Formula were permitted.
• Additionally, no electrons can be present between the shells.
• The mathematical expression for the permitted value of the atomic radius in the energy level is,
  r(n) = n² + r(1)

As a result, the equation for energy state for radius is often known as Bohr's formula.