Atoms

Step 1: Understanding the Concept:
In the Bohr model of the atom, there is a fixed numerical relationship between Kinetic Energy ( ), Potential Energy ( ), and Total Energy ( ).
Step 2: Detailed Explanation:
The relationships are: 1. 2. 3. To find the ratio : $ -1/2$.

Step 1: Understanding the Concept:
The radius of a nucleus ( ) depends on its mass number ( ) according to the empirical formula .
Step 2: Detailed Explanation:
For a Hydrogen atom, the nucleus is a single proton, so . The constant is approximately (or ). $ $
Step 3: Final Answer:
The nuclear radius is 1.2 fm.

Step 1: Understanding the Concept:
Mass and energy are interconvertible according to Einstein's mass-energy equivalence relation.
Step 2: Calculation:
Formula: Given: , . $ 9 \times 10^{16}$ J.

Step 1: Understanding the Concept:
According to Bohr's model, the radius of the orbit of a hydrogen atom is proportional to the square of the principal quantum number ( ).
Step 2: Calculation:
Formula: Given: and . $ 4.77 \times 10^{-10}$ m.