Ratio of time periods of electrons in 1st and 2nd orbits of Hydrogen is?
Solution and Explanation
The time period of an electron is given by,
\(T = n^3h^3/(4π^2mZ^2e^4)\)
For first orbit, n = 1
\(T_1 = 1^3h^3/(4π^2mZ^2e^4)\)
For second orbit, n = 2
\(T_2 = 2^3h^3/(4π^2mZ^2e^4)\)
Therefore, we have
\(T_1/T_2 = 1:8\)
The time period of an electron can be expressed as follows:
T=n3h34π2mZ2e4
For the first orbit (n = 1):
T1=13h34π2mZ2e4
For the second orbit (n = 2):
T2=23h34π2mZ2e4
Consequently,
T1T2=81
This ratio signifies a proportion of 1 to 8.
Top Questions on Structure of atom
- In case of isoelectronic species the size of \(F^-\), \(Na\) and \(Na^+\) is affected by:
- JEE Main - 2024
- Chemistry
- Structure of atom
- Wavenumber for a radiation having $5800 \, \mathring{A}$ wavelength is $x \times 10 \, \text{cm}^{-1}$. The value of $x$ is _________
- JEE Main - 2024
- Chemistry
- Structure of atom
- According to Bohr’s model, the highest kinetic energy is associated with the electron in the
- JEE Advanced - 2024
- Chemistry
- Structure of atom
- Among the following, the correct statement(s) for electrons in an atom is(are)
- JEE Advanced - 2024
- Chemistry
- Structure of atom
- The number of degenerate orbitals present in 4d subshell is
- AP POLYCET - 2024
- Chemistry
- Structure of atom
Questions Asked in BITSAT exam
- Let \( ABC \) be a triangle and \( \vec{a}, \vec{b}, \vec{c} \) be the position vectors of \( A, B, C \) respectively. Let \( D \) divide \( BC \) in the ratio \( 3:1 \) internally and \( E \) divide \( AD \) in the ratio \( 4:1 \) internally. Let \( BE \) meet \( AC \) in \( F \). If \( E \) divides \( BF \) in the ratio \( 3:2 \) internally then the position vector of \( F \) is:
- BITSAT - 2024
- Vectors
- Let \( \mathbf{a} = \hat{i} - \hat{k}, \mathbf{b} = x\hat{i} + \hat{j} + (1 - x)\hat{k}, \mathbf{c} = y\hat{i} + x\hat{j} + (1 + x - y)\hat{k} \). Then, \( [\mathbf{a} \, \mathbf{b} \, \mathbf{c}] \) depends on:}
- BITSAT - 2024
- Vectors
- Let the foot of perpendicular from a point \( P(1,2,-1) \) to the straight line \( L : \frac{x}{1} = \frac{y}{0} = \frac{z}{-1} \) be \( N \). Let a line be drawn from \( P \) parallel to the plane \( x + y + 2z = 0 \) which meets \( L \) at point \( Q \). If \( \alpha \) is the acute angle between the lines \( PN \) and \( PQ \), then \( \cos \alpha \) is equal to:
- The magnitude of projection of the line joining \( (3,4,5) \) and \( (4,6,3) \) on the line joining \( (-1,2,4) \) and \( (1,0,5) \) is:
- BITSAT - 2024
- Vectors
- The angle between the lines whose direction cosines are given by the equations \( 3l + m + 5n = 0 \) and \( 6m - 2n + 5l = 0 \) is:
- BITSAT - 2024
- Vectors
Concepts Used:
Structure of Atom
Atomic Structure:
The atomic structure of an element refers to the constitution of its nucleus and the arrangement of the electrons around it. Primarily, the atomic structure of matter is made up of protons, electrons and neutrons.
Dalton’s Atomic Theory
Dalton proposed that every matter is composed of atoms that are indivisible and indestructible.
The following are the postulates of his theory:
- Every matter is made up of atoms.
- Atoms are indivisible.
- Specific elements have only one type of atoms in them.
- Each atom has its own constant mass that varies from element to element.
- Atoms undergo rearrangement during a chemical reaction.
- Atoms can neither be created nor be destroyed but can be transformed from one form to another.
Cons of Dalton’s Atomic Theory
- The theory was unable to explain the existence of isotopes.
- Nothing about the structure of atom was appropriately explained.
- Later, the scientists discovered particles inside the atom that proved, the atoms are divisible.
Subatomic Particles
- Protons - are positively charged subatomic particles.
- Electron - are negatively charged subatomic particles.
- Neutrons - are electrically neutral particles and carry no charge
Atomic Structure of Isotopes
Several atomic structures of an element can exist, which differ in the total number of nucleons.These variants of elements having a different nucleon number (also known as the mass number) are called isotopes of the element. Therefore, the isotopes of an element have the same number of protons but differ in the number of neutrons. For example, there exist three known naturally occurring isotopes of hydrogen, namely, protium, deuterium, and tritium.