Home
Class 11
CHEMISTRY
psi(1s)=(1)/(sqrt(pia(0)^(3//2)))e^((r )...

`psi_(1s)=(1)/(sqrt(pia_(0)^(3//2)))e^((r )/(a_(0)))`
Find the distance `r` from nucleous at which `e^(-)` finding probability is max. [For H-atom]`a_(0)rarrI` Bohr radius

Text Solution

Verified by Experts

`p(r )=4pi^(2)psi^(2)=4pir^(2)xx(1)/(pia_(0)^(3))xxe^((Zr)/(a_(0)))`
for maxima or minima.
`(d)/(dr)[p(r )]=0`
`(4)/(a_(0)^(3))(d)/(dr)(r^(2)e^((Zr)/(a_(0))))=0`
`[-r^(2)xxe^((Zr)/(a_(0)))xx(Z)/(a_(0))]+2re^((Zr)/(a_(0)))=0`
`Zre.^(Zr)/(a_(0))[1-(r )/(a_(0))]=0`
`r=a_(0) = 0.529Å`
Promotional Banner

Topper's Solved these Questions

  • ATOMIC STRUCTURE

    ALLEN|Exercise Exercise - 01|38 Videos

  • ATOMIC STRUCTURE

    ALLEN|Exercise Exercise - 02|59 Videos

  • IUPAC NOMENCLATURE

    ALLEN|Exercise Exercise - 05(B)|8 Videos

Similar Questions

Explore conceptually related problems

Consider psi (wave function) of 2s atomic orbital of H-atom is- psi_(2s)=(1)/(4sqrt(2pia_(0)^(3//2)))[2-(r )/(a_(0))]e^.(r )/(2a_(0) Find distance of radial node from nucleous in terms of a_(0)

The wave function of 2s electron is given by W_(2s) = (1)/(4sqrt(2pi))((1)/(a_(0)))^(3//2)(2 - (r )/(a_(0)))e^(-1 a0) It has a node at r = r_(p) .Find the radiation between r_(p) and a

According to qauntum mechanical model of H-like species, and electron can be represented by a wave function (psi) which contain all dynamic information about the electron. The nature of wave function depends on the type of the orbital to which the electron belongs. For an orbital psi=[sqrt(2)/(81sqrt(3pi))]((1)/(a_(0)))^(3//2)(27-18sigma+2sigma^(2))e^((sigma)/(3)) Where, sigma =((Zr)/(a_(0))),r = radial distance from nucleous, a_(0)=52.9pm Which of the following represents the position of one of the radial nodes?

The wave function for 1s orbital of hydrogen atom is given by: Psi_(1s)=(pi)/sqrt2e^(-r//a_(0)) Where, a_(0) = Radius of first Bohar orbit r= Distance from the nucleus (Probability of finding the ekectron varies with respect to it) What will be the ratio of probability of finding rhe electron at the nucleus to first Bohr's orbit a_(0) ?

a.The schrodinger wave equation for hydrogen atom is psi_(2s) = (1)/(4sqrt(2pi)) ((1)/(a_(0)))^((3)/(2)) (2 - (r_(0))/(a_(0)))e^((-(r )/(a)) When a_(0) is Bohr's radius Let the radial node in 2s be n at Then find r_(0) in terms of a_(0) b. A base ball having mass 100 g moves with velocity 100 m s^(-1) .Find the value of teh wavelength of teh base ball

[" The Schrodinger wave equation "],[" for hydrogen atom is: "],[qquad [psi_(2s)=(1)/(4sqrt(2 pi))((1)/(a_(0)))^(3/2)(2-(r_(0))/(a_(0)))e^((-r_(0))/(a_(0))),],[" where "a_(0)" is Bohr's radius.If the "],[" radial node is "2s" be at "r_(0)," then the "],[" value of "(r_(0))/(a_(0))" is "]]

The Schrodinger wave equation for hydrogen atom is Psi_(2s) = (1)/(4sqrt(2pi)) ((1)/(a_(0)))^(3//2) (2 - (r)/(a_(0))) e^(-r//a_(0)) , where a_(0) is Bohr's radius . If the radial node in 2s be at r_(0) , then r_(0) would be equal to :

ALLEN-ATOMIC STRUCTURE-Exercise - 05[A]
  1. psi(1s)=(1)/(sqrt(pia(0)^(3//2)))e^((r )/(a(0))) Find the distance r...

    Text Solution

    |

  2. An atom has a mass of 0.02kg and uncertainty in its velocity is 9.218x...

    Text Solution

    |

  3. Energy of H-atom in the ground state is -13.6eV. Hence energy in the s...

    Text Solution

    |

  4. Uncertainty in position of a particle of 25g in space is 10^(8)m Henc...

    Text Solution

    |

  5. The orbital angular momentum for an electron revolving in an orbit ...

    Text Solution

    |

  6. The number of d-electron retained in Fe^(2) ("At no. of" Fe =26) ion ...

    Text Solution

    |

  7. The de-Broglie wavelength of a tennis ball mass 60 g moving with a ve...

    Text Solution

    |

  8. In Bohr series of lines of hydrogen spectrum, third line from the red ...

    Text Solution

    |

  9. Which of the following sets of quantum number is correct for an electr...

    Text Solution

    |

  10. Consider the ground state Cr atom (Z = 24). The number of electron w...

    Text Solution

    |

  11. The wavelength of the radiations emitted when in a hydrogen atom elect...

    Text Solution

    |

  12. Which one of the following sets of ions represents the collection of i...

    Text Solution

    |

  13. In a malti-electrons atom which of the following orbitals deseribed...

    Text Solution

    |

  14. Which of the following are not isoelectronic speices ?

    Text Solution

    |

  15. Which of the following statement is correct in relation to the hydroge...

    Text Solution

    |

  16. According to Boohr's theory the angular momentum of an electron in 5th...

    Text Solution

    |

  17. Uncertainty in the position of an electron mass (9. 1 xx 10^(31) kg) ...

    Text Solution

    |

  18. Which of the following sets of quantum numbers represents the highest ...

    Text Solution

    |

  19. Which one of the following consitutes a group of the isoelectronic spe...

    Text Solution

    |

  20. The ionization enthalpy of hydrogen atom is 1.312 xx 10^6 J mol^-1. Th...

    Text Solution

    |

  21. In an atom, an electron is moving with a speed of 600 m//s with an ac...

    Text Solution

    |