Atomic Structure

The wave function ${\mathrm{\psi}}_{\mathrm{n},l,{\mathrm{m}}_{1}}$is a mathematical function whose value depends upon spherical polar coordinates (r, θ, ϕ) of the electron and characterized by the quantum numbers n, l and m

For the given orbital in column 1, the only

_{1}. Here r is distance from nucleus, θ is colatitude and ϕ is azimuth. In the mathematical functions given in the Table, Z is atomic number a_{0}is Bohr radius. Column-1 |
Column-2 |
Column-3 |

(I) 1s orbital | (i) ${\mathrm{\psi}}_{\mathrm{n},l,{\mathrm{m}}_{1}}\propto {\left(\frac{\mathrm{Z}}{{\mathrm{a}}_{0}}\right)}^{\frac{3}{2}}{\mathrm{e}}^{-\left(\frac{\mathrm{Zr}}{{\mathrm{a}}_{\mathrm{e}}}\right)}$ | |

(II) 2s orbital | (ii) One radial node | (Q) Probability density at nucleus $\propto \frac{1}{{a}_{0}^{3}}$ |

(III) 2p_{z} orbital |
(iii) ${\mathrm{\psi}}_{\mathrm{n},l,{\mathrm{m}}_{1}}\propto {\left(\frac{\mathrm{Z}}{{\mathrm{a}}_{0}}\right)}^{\frac{5}{2}}{\mathrm{re}}^{-\left(\frac{\mathrm{Zr}}{2{\mathrm{a}}_{\mathrm{e}}}\right)}\mathrm{cos\theta}$ | (R) Probability density is maximum at nucleus |

(IV) $3{\mathrm{d}}_{\mathrm{z}}^{2}$ orbital | (iv) xy - plane is a nodal plane | (S) Energy needed to excite electron from n = 2 state to n = 4 state is $\frac{27}{32}$ times the energy needed to excite electron from n = 2 state to n = 6 state |

For the given orbital in column 1, the only

**CORRECT**combination for any hydrogen - like species is :
View Solution

JEE Advanced 2017

The wave function ${\mathrm{\psi}}_{\mathrm{n},l,{\mathrm{m}}_{1}}$is a mathematical function whose value depends upon spherical polar coordinates (r, θ, ϕ) of the electron and characterized by the quantum numbers n, l and m

For He

_{1}. Here r is distance from nucleus, θ is colatitude and ϕ is azimuth. In the mathematical functions given in the Table, Z is atomic number a_{0}is Bohr radius. Column-1 |
Column-2 |
Column-3 |

(I) 1s orbital | (i) ${\mathrm{\psi}}_{\mathrm{n},l,{\mathrm{m}}_{1}}\propto {\left(\frac{\mathrm{Z}}{{\mathrm{a}}_{0}}\right)}^{\frac{3}{2}}{\mathrm{e}}^{-\left(\frac{\mathrm{Zr}}{{\mathrm{a}}_{\mathrm{e}}}\right)}$ | |

(II) 2s orbital | (ii) One radial node | (Q) Probability density at nucleus $\propto \frac{1}{{a}_{0}^{3}}$ |

(III) 2p_{z} orbital |
(iii) ${\mathrm{\psi}}_{\mathrm{n},l,{\mathrm{m}}_{1}}\propto {\left(\frac{\mathrm{Z}}{{\mathrm{a}}_{0}}\right)}^{\frac{5}{2}}{\mathrm{re}}^{-\left(\frac{\mathrm{Zr}}{2{\mathrm{a}}_{\mathrm{e}}}\right)}\mathrm{cos\theta}$ | (R) Probability density is maximum at nucleus |

(IV) $3{\mathrm{d}}_{\mathrm{z}}^{2}$ orbital | (iv) xy - plane is a nodal plane | (S) Energy needed to excite electron from n = 2 state to n = 4 state is $\frac{27}{32}$ times the energy needed to excite electron from n = 2 state to n = 6 state |

For He

^{+}ion, the only**INCORRECT**combination is
View Solution

JEE Advanced 2017

The wave function ${\mathrm{\psi}}_{\mathrm{n},l,{\mathrm{m}}_{1}}$is a mathematical function whose value depends upon spherical polar coordinates (r, θ, ϕ) of the electron and characterized by the quantum numbers n, l and m

For hydrogen atom, the only

_{1}. Here r is distance from nucleus, θ is colatitude and ϕ is azimuth. In the mathematical functions given in the Table, Z is atomic number a_{0}is Bohr radius. Column-1 |
Column-2 |
Column-3 |

(I) 1s orbital | (i) ${\mathrm{\psi}}_{\mathrm{n},l,{\mathrm{m}}_{1}}\propto {\left(\frac{\mathrm{Z}}{{\mathrm{a}}_{0}}\right)}^{\frac{3}{2}}{\mathrm{e}}^{-\left(\frac{\mathrm{Zr}}{{\mathrm{a}}_{\mathrm{e}}}\right)}$ | |

(II) 2s orbital | (ii) One radial node | (Q) Probability density at nucleus $\propto \frac{1}{{a}_{0}^{3}}$ |

(III) 2p_{z} orbital |
(iii) ${\mathrm{\psi}}_{\mathrm{n},l,{\mathrm{m}}_{1}}\propto {\left(\frac{\mathrm{Z}}{{\mathrm{a}}_{0}}\right)}^{\frac{5}{2}}{\mathrm{re}}^{-\left(\frac{\mathrm{Zr}}{2{\mathrm{a}}_{\mathrm{e}}}\right)}\mathrm{cos\theta}$ | (R) Probability density is maximum at nucleus |

(IV) $3{\mathrm{d}}_{\mathrm{z}}^{2}$ orbital | (iv) xy - plane is a nodal plane | (S) Energy needed to excite electron from n = 2 state to n = 4 state is $\frac{27}{32}$ times the energy needed to excite electron from n = 2 state to n = 6 state |

For hydrogen atom, the only

**CORRECT**combination is
View Solution

JEE Advanced 2017

The work function of some metals is listed below. The number of metals which will show photoelectric effect when light of 300nm was wavelength falls on the metals is

Metal |
Li |
Na |
K |
Mg |
Cu |
Ag |
Fe |
Pt |
W |

2.4 |
2.3 |
2.2 |
3.7 |
4.8 |
4.3 |
4.7 |
6.3 |
4.75 |

View Solution

JEE Advanced 2011