Atoms And Nuclei

Given , the frequency of the incident light is related to the energy absorbed by the hydrogen atoms using the equation: Where:
- is the energy absorbed,
- is Planck's constant,
- is the frequency of the incident light.

The total emission lines are 6, so the electron must have absorbed energy and jumped from to . The energy difference between these levels can be expressed as: Using the formula for the frequency, we calculate: Now solving for the frequency: Thus, .

Step 1: Understanding the Concept:
Mass defect ( ) is the difference between the total mass of the constituent nucleons (protons and neutrons) and the actual experimental mass of the atom. Carbon-12 has 6 protons and 6 neutrons.
: Key Formula or Approach:
.
Energy equivalent .
Step 2: Detailed Explanation:
For :
Number of protons .
Number of neutrons .
Total mass of nucleons:

.
Experimental mass .
Mass defect:
.
Convert mass defect to MeV/ :

.
Step 3: Final Answer:
The mass defect is 89.03 MeV/ .

Concept: According to Bohr's quantization condition:
Step 1:Given angular momentum} Substitute in Bohr relation: Multiply both sides by :
Step 2:Energy of electron in hydrogen atom}
Step 3:Substitute }

Step 1: Understanding the Question:
We need to identify the initial and final orbit numbers ( ) using the radius ratio and then calculate the emission wavelength using the Rydberg formula.
Step 2: Key Formula or Approach:
1. Radius .
2. Rydberg formula: .
Step 3: Detailed Explanation:
Ratio of radii: .
Taking the square root: .
The transition is to a lower orbit, so possible values could be or .
From the ratio , the most direct interpretation is and .
Now apply the Rydberg formula for (Balmer series):



Step 4: Final Answer:
The wavelength is approximately 486 nm.

The binding energy per nucleon is given by the formula: The mass defect is the difference between the mass of the nucleus and the sum of the masses of its constituent nucleons. The mass defect is given by: Substituting the given values into this equation, the binding energy per nucleon is: After performing the necessary calculations, we find that the binding energy per nucleon for is 6.94 MeV.
Final Answer: 6.94 MeV