In a hydrogen atom, the electron is in $n^{th}$ excited state. It may come down to second excited state by emitting ten different wavelengths. What is the value of $n$ :
In a hydrogen atom, the electron is in $n^{th}$ excited state. It may come down to second excited state by emitting ten different wavelengths. What is the value of $n$ :
- A
$6$
- B
$7$
- C
$8$
- D
$5$
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Apply Bohr’s atomic model to a lithium atom. Assuming that its two $K$-shell electrons are too close to nucleus such that nucleus and $K$-shell electron act as a nucleus of effective positive charge equivalent to electron. The ionization energy of its outermost electron is......$eV$
Apply Bohr’s atomic model to a lithium atom. Assuming that its two $K$-shell electrons are too close to nucleus such that nucleus and $K$-shell electron act as a nucleus of effective positive charge equivalent to electron. The ionization energy of its outermost electron is......$eV$
When the accelerating voltage applied on the electrons increased beyond a critical value
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Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of nature and see if we can get a quantity with the dimensions of length that is roughly equal to the known size of an atom $\left(\sim 10^{-10} \;m \right)$
$(a)$ Construct a quantity with the dimensions of length from the fundamental constants $e, m_{e},$ and $c .$ Determine its numerical value.
$(b)$ You will find that the length obtained in $(a)$ is many orders of magnitude smaller than the atomic dimensions. Further, it involves $c .$ But energies of atoms are mostly in non-relativistic domain where $c$ is not expected to play any role. This is what may have suggested Bohr to discard $c$ and look for 'something else' to get the right atomic size. Now, the Planck's constant $h$ had already made its appearance elsewhere. Bohr's great insight lay in recognising that $h, m_{e},$ and $e$ will yield the right atomic size. Construct a quantity with the dimension of length from $h m_e$, and $e$ and confirm that its numerical value has indeed the correct order of magnitude.
Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of nature and see if we can get a quantity with the dimensions of length that is roughly equal to the known size of an atom $\left(\sim 10^{-10} \;m \right)$
$(a)$ Construct a quantity with the dimensions of length from the fundamental constants $e, m_{e},$ and $c .$ Determine its numerical value.
$(b)$ You will find that the length obtained in $(a)$ is many orders of magnitude smaller than the atomic dimensions. Further, it involves $c .$ But energies of atoms are mostly in non-relativistic domain where $c$ is not expected to play any role. This is what may have suggested Bohr to discard $c$ and look for 'something else' to get the right atomic size. Now, the Planck's constant $h$ had already made its appearance elsewhere. Bohr's great insight lay in recognising that $h, m_{e},$ and $e$ will yield the right atomic size. Construct a quantity with the dimension of length from $h m_e$, and $e$ and confirm that its numerical value has indeed the correct order of magnitude.
Energy levels $A, B$ and $C$ of a certain atom correspond to increasing values of energy, i.e. $E_A < E_B < E_C$ . If $\lambda _1, \lambda _2$ and $\lambda _3$ are the wavelengths of radiations corresponding to transitions $C$ to $B, B$ to $A$ and $C$ to $A$ respectively , which of the following relations is correct ?
Energy levels $A, B$ and $C$ of a certain atom correspond to increasing values of energy, i.e. $E_A < E_B < E_C$ . If $\lambda _1, \lambda _2$ and $\lambda _3$ are the wavelengths of radiations corresponding to transitions $C$ to $B, B$ to $A$ and $C$ to $A$ respectively , which of the following relations is correct ?
Give a powerful way to determine an upper limit to the size of the electron.
Give a powerful way to determine an upper limit to the size of the electron.