To find the radius of the electron in the 4th Bohr’s orbit of hydrogen in terms of \( R \), the radius in the 3rd orbit, we can use the relation of radii of Bohr’s orbits:

\[ R_n = \frac{n^2}{Z} R \]

where:
– \( R_n \) is the radius of the nth orbit,
– \( n \) is the principal quantum number,
– \( Z \) is the atomic number (for hydrogen, \( Z = 1 \)),
– \( R \) is the radius in the first orbit.

Given that the electron is initially in the 3rd orbit (\( n = 3 \)), we have:

\[ R_3 = \frac{3^2}{1} R = 9R \]

Now, to find the radius in the 4th orbit (\( n = 4 \)), we use the same formula:

\[ R_4 = \frac{4^2}{1} R = 16R \]

Therefore, the radius of the electron in the 4th orbit in terms of \( R \) is \( 16R \), which corresponds to option 2) \( \left(\frac{16}{9}\right)R \).