1. Use the node formulas for atomic orbitals

For an orbital with quantum numbers $n$ and $l$:

• Angular nodes $= l$
• Radial nodes $= n - l - 1$

2. Given condition: no angular nodes

No angular nodes means:

$l = 0$

So the orbital must be an $s$-orbital.

3. Given condition: two radial nodes

Using

$n - l - 1 = 2$

Since $l=0$ for an $s$-orbital:

$n - 0 - 1 = 2$ $n - 1 = 2$ $n = 3$

So the orbital is:

$3s$

4. Check options

• A: $2s$
  Radial nodes $= 2-0-1=1$ ❌

• B: $3s$
  Radial nodes $= 3-0-1=2$ and angular nodes $=0$ ✅

• C: $3p$
  Angular nodes $=1$ ❌

• D: $2p$
  Angular nodes $=1$ ❌

5. Final answer

The required orbital is $3s$.