Home
Class 12
PHYSICS
For the hydrogen atom in its ground stat...

For the hydrogen atom in its ground state, calculate (a) the probability density y (r) and (b) the radial probability density `Psi^(2)(r)` for r= a, where a is the Bohr radius.

Text Solution

Verified by Experts

(a) `291nm^(-3)`, (b) `10.2nm^(-1)`
Promotional Banner

Topper's Solved these Questions

  • HYDROGEN ATOM

    RESNICK AND HALLIDAY|Exercise PRACTICE QUESTIONS (Single Correct Choice Type)|51 Videos
  • HYDROGEN ATOM

    RESNICK AND HALLIDAY|Exercise PRACTICE QUESTIONS (More than One Correct Choice Type)|15 Videos
  • HYDROGEN ATOM

    RESNICK AND HALLIDAY|Exercise CHECKPOINT|6 Videos
  • HEAT-MEASUREMENT AND TRANSFER

    RESNICK AND HALLIDAY|Exercise PRACTICE QUESTIONS( INTEGER TYPE)|5 Videos
  • INTERFERENCE AND DIFFRACTION

    RESNICK AND HALLIDAY|Exercise PRACTICE QUESTIONS (Integer Type)|6 Videos

Similar Questions

Explore conceptually related problems

The radius of hydrogen atom, in its ground state, is of the order of

Calculate the radial probability density P(r) for the hydro- gen atom in its ground state at (a) r = 0, (b) r = a, and (c) r= 2a, where a is the Bohr radius.

Show that the radial probability density for the ground state of the hydrogen atom has maximum at r = a.

The maximum radial probability in 1s -orbital occures at a distance when : [r_(0)= "Bohr radius"]

If an orbital electron of the hydrogen atom jumps from the groud state to a higher energy state, its orbital value. If the radius of the electron orbit in the ground state is r , then the radius of the new orbit would be:

In a certain electronic transition in the hydrogen atoms from an initial state (1) to a final state (2) , the difference in the orbit radius ((r_(1)-r_(2)) is 24 times the first Bohr radius. Identify the transition-

RESNICK AND HALLIDAY-HYDROGEN ATOM-PROBLEMS
  1. How much energy is required to cause an electron of hydrogen to move f...

    Text Solution

    |

  2. A particle is confined to the one-dimensional infinite potential well ...

    Text Solution

    |

  3. For the hydrogen atom in its ground state, calculate (a) the probabili...

    Text Solution

    |

  4. Light of wavelength 102.6 nm is emitted by a hydrogen atom. What are t...

    Text Solution

    |

  5. What are the (a) energy. (b) magnitude of the momentum, and (c) wavele...

    Text Solution

    |

  6. What are the (a) wavelength range and (b) frequency range of the Lyman...

    Text Solution

    |

  7. An electron is trapped in a one-dimensional infinite potential well. F...

    Text Solution

    |

  8. Suppose that a hydrogen atom in the ground state absorbs photons of wa...

    Text Solution

    |

  9. A proton is confined to a one-dimensional infinite potential well 120 ...

    Text Solution

    |

  10. An electron is trapped in a one-dimensional infinite potential well. F...

    Text Solution

    |

  11. For what value of the principal quantum number n would the effective r...

    Text Solution

    |

  12. A hydrogen atom is excited from its ground state to the state with n =...

    Text Solution

    |

  13. An electron is trapped in a one-dimensional infinite potential well th...

    Text Solution

    |

  14. An electron in a one-dimensional infinite potential well of length L h...

    Text Solution

    |

  15. Consider an atomic nucleus to be equivalent to a one- dimensional infi...

    Text Solution

    |

  16. (a) What is the energy E of the hydrogen-atom electron whose probabili...

    Text Solution

    |

  17. What is the ground-state energy of (a) an electron and (b) a proton if...

    Text Solution

    |

  18. What must be the width of a one-dimensional infinite potential well if...

    Text Solution

    |

  19. An electron is trapped in a one-dimensional infinite well of width 200...

    Text Solution

    |

  20. Hydrogen atoms are in an excited state with n = 5. In terms of the Boh...

    Text Solution

    |