Physics
posted by Kat .
In a hydrogen atom, if the radius of the orbit of the electron is doubled, then its energy will ...
>> Increase by a factor of 2??

The radius of a Bohr orbit increases with the square of the quantum number, n. So the principal quantum number would have to increase by a factor of sqrt2. This will not be possible since the quantum number must remain an integer.
Your teacher may not be aware of this.
In general, the total energy of a Bohr orbit becomes larger (less nagative) when the radius of the orbit increases. A totally detached electron (infinite radius) has an energy of zero. 
Actually "Actually, it is not possible for the radius of the orbit to double"
is one of the options, so is that right for the reason you stated?