The number of atomic orbitals from the following having 5 radial nodes is ___________.

$7 \mathrm{s}, 7 \mathrm{p}, 6 \mathrm{s}, 8 \mathrm{p}, 8 \mathrm{d}$

<p>Radial nodes in an atomic orbital are areas where the probability of finding an electron is zero. The number of radial nodes in an orbital is given by the formula: </p> <p>$ \text{number of radial nodes} = n - l - 1 $</p> <p>where $n$ is the principal quantum number and $l$ is the azimuthal quantum number. The azimuthal quantum number ($l$) can have values from 0 to $n-1$, and it determines the shape of the orbital (s, p, d, f, etc.). For an s orbital, $l=0$; for a p orbital, $l=1$; for a d orbital, $l=2$; and so on.</p> <p>Let&#39;s calculate the number of radial nodes for each given orbital:</p> <ol> <li>7s: $n=7$, $l=0$, so the number of radial nodes is $7 - 0 - 1 = 6$, not 5.</li> <li>7p: $n=7$, $l=1$, so the number of radial nodes is $7 - 1 - 1 = 5$.</li> <li>6s: $n=6$, $l=0$, so the number of radial nodes is $6 - 0 - 1 = 5$.</li> <li>8p: $n=8$, $l=1$, so the number of radial nodes is $8 - 1 - 1 = 6$, not 5.</li> <li>8d: $n=8$, $l=2$, so the number of radial nodes is $8 - 2 - 1 = 5$.</li> </ol> <p>Therefore, the orbitals with 5 radial nodes are 7p, 6s, and 8d, so there are 3 such orbitals.</p>