हिंदी
कर्नाटक बोर्ड पी.यू.सी.पीयूसी विज्ञान कक्षा ११

The Bohr Radius is Given by a 0 = ∈ 0 H 2 π M E 2 . Verify that the Rhs Has Dimensions of Length.

Advertisements
Advertisements

प्रश्न

The Bohr radius is given by  `a_0 = (∈_0h^2)/{pime^2}`. Verify that the RHS has dimensions of length.

टिप्पणी लिखिए
Advertisements

उत्तर

The dimensions of ε0 can be derived from the formula given below:
`a = (epsilon_0h^2)/(pime^2) = (A^2T^0(ML^2 T^-1)^2)/(L^2ML^-2 (AT)^2)`

`=(M^2L^2T^-2)/(M^2L^3T^-2) = L`
Clearly, a0 has the dimensions of length.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 43: Bohr’s Model and Physics of Atom - Exercises [पृष्ठ ३८४]

APPEARS IN

एचसी वर्मा Concepts of Physics Volume 1 and 2 [English]
अध्याय 43 Bohr’s Model and Physics of Atom
Exercises | Q 1 | पृष्ठ ३८४

संबंधित प्रश्न

Find the frequency of revolution of an electron in Bohr’s 2nd orbit; if the radius and speed of electron in that orbit is 2.14 × 10-10 m and 1.09 × 106 m/s respectively. [π= 3.142]


What is the maximum number of emission lines when the excited electron of an H atom in n = 6 drops to the ground state?


If the velocity of the electron in Bohr’s first orbit is 2.19 × 106 ms-1, calculate the de Broglie wavelength associated with it.


State Bohr postulate of hydrogen atom that gives the relationship for the frequency of emitted photon in a transition.


Calculate the de-Broglie wavelength associated with the electron revolving in the first excited state of the hydrogen atom. The ground state energy of the hydrogen atom is −13.6 eV.


In Bohr model of hydrogen atom, which of the following is quantised?


According to Bohr's model of hydrogen atom, an electron can revolve round a proton indefinitely, if its path is ______.


Ratio of longest to shortest wavelength in Balmer series is ______.


Calculate the energy and frequency of the radiation emitted when an electron jumps from n = 3 to n = 2 in a hydrogen atom.


The wavelength of the first time line of Ballmer series is 6563 A°. The Rydberg constant for hydrogen is about:-


The binding energy of a H-atom, considering an electron moving around a fixed nuclei (proton), is B = `- (Me^4)/(8n^2ε_0^2h^2)`. (m = electron mass). If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be

B = `- (Me^4)/(8n^2ε_0^2h^2)` (M = proton mass)

This last expression is not correct because ______.


Consider aiming a beam of free electrons towards free protons. When they scatter, an electron and a proton cannot combine to produce a H-atom ______.

  1. because of energy conservation.
  2. without simultaneously releasing energy in the from of radiation.
  3. because of momentum conservation.
  4. because of angular momentum conservation.

The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10–11m. The radius of the n = 3 orbit is ______.


Use Bohr's postulate to prove that the radius of nth orbit in a hydrogen atom is proportional to n2.


In Bohr's atomic model of hydrogen, let K. P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level:


In hydrogen atom, transition from the state n = 6 to n = 1 results in ultraviolet radiation. Infrared radiation will be obtained in the transition ______.


Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is ______.


The figure below is the Energy level diagram for the Hydrogen atom. Study the transitions shown and answer the following question:

  1. State the type of spectrum obtained.
  2. Name the series of spectrum obtained.


Which from following is CORREСТ relationship between wavelength and momentum of electron?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×