If the densities of nuclei of `""_(1) H^(1)` and `""_(92) U^(238)` are X and Y respectively ,then correct relation is

Options

A. X = Y
B. ` X lt Y`
C. Y = 92 X
D. Y = 238 X

Explanation

To solve the question regarding the densities of the nuclei of hydrogen and uranium-238, we will follow these steps:

### Step 1: Understand the Concept of Nuclear Density
Nuclear density is defined as the mass of the nucleus divided by its volume. It is important to note that the density of atomic nuclei is approximately constant for all elements, regardless of their size or atomic mass.

### Step 2: Identify the Nuclei in the Question
We have two nuclei to consider:
- Hydrogen nucleus (denoted as \( _{1}^{1}H \))
- Uranium-238 nucleus (denoted as \( _{92}^{238}U \))

### Step 3: Recall the Density Relation
The density \( \rho \) of a nucleus can be expressed as:
\[ \rho = \frac{mass}{volume} \]
For atomic nuclei, the volume can be approximated using the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the nucleus. The radius of a nucleus can be estimated using the formula:
\[ r = r_0 A^{1/3} \]
where \( A \) is the mass number and \( r_0 \) is a constant (approximately \( 1.2 \, \text{fm} \)).

### Step 4: Compare the Densities
Since the density of nuclei is approximately constant across different elements, we can conclude:
\[ x = y \]
where \( x \) is the density of the hydrogen nucleus and \( y \) is the density of the uranium-238 nucleus.

### Step 5: State the Final Relation
Thus, the correct relation between the densities of the nuclei of hydrogen and uranium-238 is:
\[ x = y \]