Give cell is `{:([Ni|Ni^(2+) ||Cu^(2+)|Cu]),(" (0.01m) (0.1m)"):}`
`E_("cell")= 0.59V`
Write Nernst equation and find `E_("N_(i)^(2+)//N_(l))^(@)` of cell. (At anode) `E_(Cu^(2+)//Cu)^(@)= 0.39V`

Explanation

`"Oxd"^(n)` half cell (At anode) Reaction : `Ni(s) rarr Ni_((aq))^(2+) + 2e^(-)`
`"Red"^(n)` half cell (At Cathode) Reaction: `ul(Cu_((aq))^(2+) + 2e^(-) rarr Cu(s))`
Overall cell Reaction: `Ni(s) + Cu_((aq))^(2+) rarr Ni^(2+) (aq) + Cu(s)`
`E_("cell") [E_((Cu^(2+)|Cu))^(@) - E_((Ni^(2+)|Ni))^(@)]- (0.059)/(2)"log" ((0.01))/((0.1))` [Nernst equation]
`0.59 V= (0.39 V- E_((Ni^(2+)|Ni))^(@))- (0.059)/(2) log 10^(-1)`
`0.59 - 0.39 = -E_((Ni^(2+)|Ni))^(@)+ 0.0295`
`0.2 = -E_((Ni^(2+)|Ni))^(@) + 0.0295`
`E_((Ni^(2+)|Ni))^(@)= 0.0295- 0.2`
`E_((Ni^(2+)|Ni))^(@)= -0.1705V`